2x(x-24)=180

Solution for 2x(x-24)=180 equation:

2x(x-24)=180

We move all terms to the left:

2x(x-24)-(180)=0

We multiply parentheses

2x^2-48x-180=0

a = 2; b = -48; c = -180;
Δ = b2-4ac
Δ = -482-4·2·(-180)
Δ = 3744
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:

$\sqrt{\Delta}=\sqrt{3744}=\sqrt{144*26}=\sqrt{144}*\sqrt{26}=12\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-12\sqrt{26}}{2*2}=\frac{48-12\sqrt{26}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+12\sqrt{26}}{2*2}=\frac{48+12\sqrt{26}}{4}
$