x^2+3x-108=180

Solution for x^2+3x-108=180 equation:

x^2+3x-108=180

We move all terms to the left:

x^2+3x-108-(180)=0

We add all the numbers together, and all the variables

x^2+3x-288=0

a = 1; b = 3; c = -288;
Δ = b2-4ac
Δ = 32-4·1·(-288)
Δ = 1161
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:

$\sqrt{\Delta}=\sqrt{1161}=\sqrt{9*129}=\sqrt{9}*\sqrt{129}=3\sqrt{129}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{129}}{2*1}=\frac{-3-3\sqrt{129}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{129}}{2*1}=\frac{-3+3\sqrt{129}}{2}
$