0=a^2+13a-90

Solution for 0=a^2+13a-90 equation:

0=a^2+13a-90

We move all terms to the left:

0-(a^2+13a-90)=0

We add all the numbers together, and all the variables

-(a^2+13a-90)=0

We get rid of parentheses

-a^2-13a+90=0

We add all the numbers together, and all the variables

-1a^2-13a+90=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:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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