Quadratic Equation Calculator

Quadratic equation calculator calculates solutions for quadratic equations by the known coefficients a, b, and term c.

What is Quadratic Equation

The quadratic equation is
ax²+bx+c=0
To solve the equation, use the quadratic formula

x = ^{-b+√b²-4ac}_2a

The input value for a, b, and c could be a negative or positive number.
except a ≠ 0, as 2a is in the denominator, and 0 can't be a divisor.

Quadratic Equation Examples

There are 3 different scenarios regarding the different roots in the equation.
1. b²-4ac=0
There is only one solution for x.
For example,
4x²+12x+9=0
In this case,
a = 4, b=12, c = 9.
Therefore
b²-4ac
=12²-4x4x9
=0

Then solve for the x using the formula.

x = ^{-b+√b²-4ac}_2a

x = ^-12+√0_2x4

x = -1.5

2. b²-4ac>0
There are two solutions for x.
For example,
5x²+8x-13=0
in this case,
a = 5, b = 8, c =-13.
Therefore
b²-4ac
=8²-4x5x(-13)
=324.

Then we use the quadratic formula to solve x.

x = ^{-b+√b²-4ac}_2a

x = ^-8+√324₁₀

x = -8+1810
x = 1 or x = -2.6

3. b²-4ac<0
There are two solutions with imaginary unit i.
For example,
5x²-10x+25=0
in this case,
a = 5, b = -10, c=25
Therefore
b²-4ac
=(-10)²-4x5x25
=100-500
=-400

Then we use the quadratic formula to solve for x.

x = ^{-b+√b²-4ac}_2a

x = ^10+√-400_2x5

x = 10+20i2x5
x = 1+2i or x = 1-2i