8x(4x+60)=180

Solution for 8x(4x+60)=180 equation:

8x(4x+60)=180

We move all terms to the left:

8x(4x+60)-(180)=0

We multiply parentheses

32x^2+480x-180=0

a = 32; b = 480; c = -180;
Δ = b2-4ac
Δ = 4802-4·32·(-180)
Δ = 253440
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:

$\sqrt{\Delta}=\sqrt{253440}=\sqrt{2304*110}=\sqrt{2304}*\sqrt{110}=48\sqrt{110}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(480)-48\sqrt{110}}{2*32}=\frac{-480-48\sqrt{110}}{64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(480)+48\sqrt{110}}{2*32}=\frac{-480+48\sqrt{110}}{64}
$