Solve Equation Calculator

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Solve Equation Calculator
Quadratic: ax² + bx + c = 0Linear: ax + b = c
Solution:
Enter values and click Solve to see the result.
function updateLabels(){var type=document.getElementById('equation_type').value;var la=document.getElementById('label_a');var lb=document.getElementById('label_b');var lc=document.getElementById('label_c');if(type==='linear'){la.innerHTML='Coefficient (a):';lb.innerHTML='Constant (b):';lc.innerHTML='Equals (c):';}else{la.innerHTML='Coefficient (a):';lb.innerHTML='Coefficient (b):';lc.innerHTML='Constant (c):';}}function calculateEquation(){var type=document.getElementById('equation_type').value;var a=parseFloat(document.getElementById('input_a').value);var b=parseFloat(document.getElementById('input_b').value);var c=parseFloat(document.getElementById('input_c').value);var showSteps=document.getElementById('steps').checked;var ans=document.getElementById('answer');if(isNaN(a)||isNaN(b)||isNaN(c)){ans.innerHTML='Please enter valid numbers in all fields.';return;}var output=";if(type==='linear'){if(a===0){if(b===c){output='Infinite solutions (Identity).';}else{output='No solution (Contradiction).';}}else{var x=(c-b)/a;output='x = '+x.toFixed(4)+'';if(showSteps){output+='
Steps:
1. Equation: '+a+'x + '+b+' = '+c+'
2. Subtract '+b+' from both sides: '+a+'x = '+(c-b)+'
3. Divide by '+a+': x = '+(c-b)+'/'+a+'
4. Result: x = '+x.toFixed(4)+'
';}}}else{if(a===0){output='Since a=0, this is a linear equation. Solving: '+b+'x + '+c+' = 0. Result: x = '+(-c/b).toFixed(4);}else{var disc=(b*b)-(4*a*c);if(disc>0){var x1=(-b+Math.sqrt(disc))/(2*a);var x2=(-b-Math.sqrt(disc))/(2*a);output='Two distinct real roots:
x₁ = '+x1.toFixed(4)+'
x₂ = '+x2.toFixed(4)+'';}else if(disc===0){var x=-b/(2*a);output='One repeated real root:
x = '+x.toFixed(4)+'';}else{var realPart=(-b/(2*a)).toFixed(4);var imagPart=(Math.sqrt(-disc)/(2*a)).toFixed(4);output='Two complex roots:
x₁ = '+realPart+' + '+imagPart+'i
x₂ = '+realPart+' – '+imagPart+'i';}if(showSteps){output+='
Steps (Quadratic Formula):
1. Disc (D) = b² – 4ac = ('+b+')² – 4('+a+')('+c+') = '+disc+'
2. x = [-b ± √D] / 2a
3. x = [-('+b+') ± √'+disc+'] / '+(2*a)+'
4. Simplify to find roots.
';}}}ans.innerHTML=output;}

How to Use the Solve Equation Calculator

The solve equation calculator is a powerful tool designed to find the unknown variable (x) in both linear and quadratic mathematical statements. Whether you are dealing with a simple first-degree equation or a complex polynomial of the second degree, this tool provides instant answers and optional step-by-step breakdowns.

Select Equation Type
Choose between "Linear" (ax + b = c) for simple relationships or "Quadratic" (ax² + bx + c = 0) for parabolic equations.
Coefficient (a)
The number multiplying the highest power of x. For quadratic equations, 'a' cannot be zero.
Coefficient (b)
The number multiplying x in the equation.
Constant (c)
The standalone number that does not have a variable attached.

The Mathematical Formulas

Our solve equation calculator uses standard algebraic methods. Understanding these formulas helps in manual verification of the results.

Linear Equations

A linear equation follows the form ax + b = c. To solve for x, we isolate the variable:

x = (c – b) / a

Quadratic Equations

A quadratic equation is expressed as ax² + bx + c = 0. The solution is found using the Quadratic Formula:

x = [-b ± √(b² – 4ac)] / 2a

The term b² – 4ac is known as the discriminant (D). It determines the nature of the roots:

  • If D > 0: Two distinct real solutions.
  • If D = 0: One real repeated solution.
  • If D < 0: Two complex (imaginary) solutions.

Calculation Examples

Example 1: Solving a Linear Equation
Equation: 3x + 9 = 21

  1. Identify: a=3, b=9, c=21
  2. Subtract b: 3x = 21 – 9 = 12
  3. Divide by a: x = 12 / 3
  4. Result: x = 4

Example 2: Solving a Quadratic Equation
Equation: x² – 5x + 6 = 0

  1. Identify: a=1, b=-5, c=6
  2. Calculate Discriminant: (-5)² – 4(1)(6) = 25 – 24 = 1
  3. Apply Formula: x = [5 ± √1] / 2
  4. Root 1: (5 + 1) / 2 = 3
  5. Root 2: (5 – 1) / 2 = 2
  6. Result: x = 3, 2

Common Questions

What is a solve equation calculator?

It is a mathematical tool that automates the process of finding the numerical value of variables in an equation. It reduces human error and handles complex components like square roots and imaginary numbers.

Can this calculator solve cubic equations?

Currently, this tool specializes in linear and quadratic equations, which are the most common in standard algebra. Cubic and quartic equations require different formulas (like Cardano's method).

What if 'a' is zero in a quadratic equation?

If the coefficient of x² is zero, the equation is no longer quadratic; it becomes linear. The solve equation calculator automatically detects this and adjusts the solving logic to provide the correct linear root.

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