3x(x-24)=180

Solution for 3x(x-24)=180 equation:

3x(x-24)=180

We move all terms to the left:

3x(x-24)-(180)=0

We multiply parentheses

3x^2-72x-180=0

a = 3; b = -72; c = -180;
Δ = b2-4ac
Δ = -722-4·3·(-180)
Δ = 7344
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:

$\sqrt{\Delta}=\sqrt{7344}=\sqrt{144*51}=\sqrt{144}*\sqrt{51}=12\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-12\sqrt{51}}{2*3}=\frac{72-12\sqrt{51}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+12\sqrt{51}}{2*3}=\frac{72+12\sqrt{51}}{6}
$