x(x-24)=180

Solution for x(x-24)=180 equation:

x(x-24)=180

We move all terms to the left:

x(x-24)-(180)=0

We multiply parentheses

x^2-24x-180=0

a = 1; b = -24; c = -180;
Δ = b2-4ac
Δ = -242-4·1·(-180)
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-36}{2*1}=\frac{-12}{2}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+36}{2*1}=\frac{60}{2}
=30
$