4x(x+24)=180

Solution for 4x(x+24)=180 equation:

4x(x+24)=180

We move all terms to the left:

4x(x+24)-(180)=0

We multiply parentheses

4x^2+96x-180=0

a = 4; b = 96; c = -180;
Δ = b2-4ac
Δ = 962-4·4·(-180)
Δ = 12096
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:

$\sqrt{\Delta}=\sqrt{12096}=\sqrt{576*21}=\sqrt{576}*\sqrt{21}=24\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(96)-24\sqrt{21}}{2*4}=\frac{-96-24\sqrt{21}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(96)+24\sqrt{21}}{2*4}=\frac{-96+24\sqrt{21}}{8}
$