Quadratic equation calculator

Quadratic equation has the basic form:

eq2
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:

-c2+34c-145=0 ... quadratic equation

D = b2 - 4ac = 576
D>0 ... The equation has two distinct real roots

c1 = 29
c2 = 5
P = {29; 5}