x^2-4+x^2-4x+5x+108=180

Solution for x^2-4+x^2-4x+5x+108=180 equation:

x^2-4+x^2-4x+5x+108=180

We move all terms to the left:

x^2-4+x^2-4x+5x+108-(180)=0

We add all the numbers together, and all the variables

2x^2+x-76=0

a = 2; b = 1; c = -76;
Δ = b2-4ac
Δ = 12-4·2·(-76)
Δ = 609
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{609}}{2*2}=\frac{-1-\sqrt{609}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{609}}{2*2}=\frac{-1+\sqrt{609}}{4}
$