2x(4x+108)=180

Solution for 2x(4x+108)=180 equation:

2x(4x+108)=180

We move all terms to the left:

2x(4x+108)-(180)=0

We multiply parentheses

8x^2+216x-180=0

a = 8; b = 216; c = -180;
Δ = b2-4ac
Δ = 2162-4·8·(-180)
Δ = 52416
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:

$\sqrt{\Delta}=\sqrt{52416}=\sqrt{576*91}=\sqrt{576}*\sqrt{91}=24\sqrt{91}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(216)-24\sqrt{91}}{2*8}=\frac{-216-24\sqrt{91}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(216)+24\sqrt{91}}{2*8}=\frac{-216+24\sqrt{91}}{16}
$