0=x^2-32x+180

Solution for 0=x^2-32x+180 equation:

0=x^2-32x+180

We move all terms to the left:

0-(x^2-32x+180)=0

We add all the numbers together, and all the variables

-(x^2-32x+180)=0

We get rid of parentheses

-x^2+32x-180=0

We add all the numbers together, and all the variables

-1x^2+32x-180=0

a = -1; b = 32; c = -180;
Δ = b2-4ac
Δ = 322-4·(-1)·(-180)
Δ = 304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-4\sqrt{19}}{2*-1}=\frac{-32-4\sqrt{19}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+4\sqrt{19}}{2*-1}=\frac{-32+4\sqrt{19}}{-2}
$