m^2-90=13m

Solution for m^2-90=13m equation:

m^2-90=13m

We move all terms to the left:

m^2-90-(13m)=0

a = 1; b = -13; c = -90;
Δ = b2-4ac
Δ = -132-4·1·(-90)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-23}{2*1}=\frac{-10}{2}
=-5
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+23}{2*1}=\frac{36}{2}
=18
$