8x(4x+24)=180

Solution for 8x(4x+24)=180 equation:

8x(4x+24)=180

We move all terms to the left:

8x(4x+24)-(180)=0

We multiply parentheses

32x^2+192x-180=0

a = 32; b = 192; c = -180;
Δ = b2-4ac
Δ = 1922-4·32·(-180)
Δ = 59904
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:

$\sqrt{\Delta}=\sqrt{59904}=\sqrt{2304*26}=\sqrt{2304}*\sqrt{26}=48\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(192)-48\sqrt{26}}{2*32}=\frac{-192-48\sqrt{26}}{64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(192)+48\sqrt{26}}{2*32}=\frac{-192+48\sqrt{26}}{64}
$