# Quadratic equation calculator

Quadratic equation has the basic form:Enter the coefficients a, b, c of quadratic equation in its basic standardized form. Solution of quadratic equations are usually two different real or complex roots, or one double root. Calculation is done by using the discriminant.

## Calculation:

$$ \smash{ c^2 = (c-9)^2+(c-8)^2 \\~\\-c^2 +34c -145 =0 \\~\\c^2 -34c +145 =0 \\~\\D = 34^2 - 4\cdot 1 \cdot 145 = 576 \\~\\D>0 \\~\\ \\~\\c_{1,2} = \frac{ 34 \pm \sqrt{ 34^2 - 4\cdot 1 \cdot 145} }{ 2 \cdot 1 } = \frac{ 34 \pm \sqrt{ 576 } }{ 2 } \\~\\c_{1,2} = \frac{ 34 \pm 24 }{ 2 } \\~\\c_{1,2} = 17 \pm 12 \\~\\c_{1} = 29 \\~\\c_{2} = 5 \\~\\ \\~\\ (c -29) (c -5) = 0 } $$

#### Solution in text:

**-c**... quadratic equation

^{2}+34c-145=0D = b

^{2}- 4ac = 576

D>0 ...

**The equation has two distinct real roots**

c

_{1}= 29

c

_{2}= 5

P = {29; 5}