2x(4x+150)=180

Solution for 2x(4x+150)=180 equation:

2x(4x+150)=180

We move all terms to the left:

2x(4x+150)-(180)=0

We multiply parentheses

8x^2+300x-180=0

a = 8; b = 300; c = -180;
Δ = b2-4ac
Δ = 3002-4·8·(-180)
Δ = 95760
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:

$\sqrt{\Delta}=\sqrt{95760}=\sqrt{144*665}=\sqrt{144}*\sqrt{665}=12\sqrt{665}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(300)-12\sqrt{665}}{2*8}=\frac{-300-12\sqrt{665}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(300)+12\sqrt{665}}{2*8}=\frac{-300+12\sqrt{665}}{16}
$