l^2-31=360

Solution for l^2-31=360 equation:

l^2-31=360

We move all terms to the left:

l^2-31-(360)=0

We add all the numbers together, and all the variables

l^2-391=0

a = 1; b = 0; c = -391;
Δ = b2-4ac
Δ = 02-4·1·(-391)
Δ = 1564
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$l_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$l_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1564}=\sqrt{4*391}=\sqrt{4}*\sqrt{391}=2\sqrt{391}$
$l_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{391}}{2*1}=\frac{0-2\sqrt{391}}{2}
=-\frac{2\sqrt{391}}{2}
=-\sqrt{391}
$
$l_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{391}}{2*1}=\frac{0+2\sqrt{391}}{2}
=\frac{2\sqrt{391}}{2}
=\sqrt{391}
$