134+2x(2x+2)=180

Solution for 134+2x(2x+2)=180 equation:

134+2x(2x+2)=180

We move all terms to the left:

134+2x(2x+2)-(180)=0

We add all the numbers together, and all the variables

2x(2x+2)-46=0

We multiply parentheses

4x^2+4x-46=0

a = 4; b = 4; c = -46;
Δ = b2-4ac
Δ = 42-4·4·(-46)
Δ = 752
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:

$\sqrt{\Delta}=\sqrt{752}=\sqrt{16*47}=\sqrt{16}*\sqrt{47}=4\sqrt{47}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{47}}{2*4}=\frac{-4-4\sqrt{47}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{47}}{2*4}=\frac{-4+4\sqrt{47}}{8}
$