x*(x-32)=180

Solution for x*(x-32)=180 equation:

x(x-32)=180

We move all terms to the left:

x(x-32)-(180)=0

We multiply parentheses

x^2-32x-180=0

a = 1; b = -32; c = -180;
Δ = b2-4ac
Δ = -322-4·1·(-180)
Δ = 1744
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:

$\sqrt{\Delta}=\sqrt{1744}=\sqrt{16*109}=\sqrt{16}*\sqrt{109}=4\sqrt{109}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-4\sqrt{109}}{2*1}=\frac{32-4\sqrt{109}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+4\sqrt{109}}{2*1}=\frac{32+4\sqrt{109}}{2}
$