x(x-52)=180

Solution for x(x-52)=180 equation:

x(x-52)=180

We move all terms to the left:

x(x-52)-(180)=0

We multiply parentheses

x^2-52x-180=0

a = 1; b = -52; c = -180;
Δ = b2-4ac
Δ = -522-4·1·(-180)
Δ = 3424
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:

$\sqrt{\Delta}=\sqrt{3424}=\sqrt{16*214}=\sqrt{16}*\sqrt{214}=4\sqrt{214}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-4\sqrt{214}}{2*1}=\frac{52-4\sqrt{214}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+4\sqrt{214}}{2*1}=\frac{52+4\sqrt{214}}{2}
$