2x(2x-1)=180

Solution for 2x(2x-1)=180 equation:

2x(2x-1)=180

We move all terms to the left:

2x(2x-1)-(180)=0

We multiply parentheses

4x^2-2x-180=0

a = 4; b = -2; c = -180;
Δ = b2-4ac
Δ = -22-4·4·(-180)
Δ = 2884
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:

$\sqrt{\Delta}=\sqrt{2884}=\sqrt{4*721}=\sqrt{4}*\sqrt{721}=2\sqrt{721}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{721}}{2*4}=\frac{2-2\sqrt{721}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{721}}{2*4}=\frac{2+2\sqrt{721}}{8}
$