5x(x-24)=180

Solution for 5x(x-24)=180 equation:

5x(x-24)=180

We move all terms to the left:

5x(x-24)-(180)=0

We multiply parentheses

5x^2-120x-180=0

a = 5; b = -120; c = -180;
Δ = b2-4ac
Δ = -1202-4·5·(-180)
Δ = 18000
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:

$\sqrt{\Delta}=\sqrt{18000}=\sqrt{3600*5}=\sqrt{3600}*\sqrt{5}=60\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-60\sqrt{5}}{2*5}=\frac{120-60\sqrt{5}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+60\sqrt{5}}{2*5}=\frac{120+60\sqrt{5}}{10}
$