2x^2+31x+15=180

Solution for 2x^2+31x+15=180 equation:

2x^2+31x+15=180

We move all terms to the left:

2x^2+31x+15-(180)=0

We add all the numbers together, and all the variables

2x^2+31x-165=0

a = 2; b = 31; c = -165;
Δ = b2-4ac
Δ = 312-4·2·(-165)
Δ = 2281
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{-(31)-\sqrt{2281}}{2*2}=\frac{-31-\sqrt{2281}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+\sqrt{2281}}{2*2}=\frac{-31+\sqrt{2281}}{4}
$