31x+x^2=180

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

31x+x^2=180

We move all terms to the left:

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

a = 1; b = 31; c = -180;
Δ = b2-4ac
Δ = 312-4·1·(-180)
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-41}{2*1}=\frac{-72}{2}
=-36
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+41}{2*1}=\frac{10}{2}
=5
$