a^2=13a-22

Solution for a^2=13a-22 equation:

a^2=13a-22

We move all terms to the left:

a^2-(13a-22)=0

We get rid of parentheses

a^2-13a+22=0

a = 1; b = -13; c = +22;
Δ = b2-4ac
Δ = -132-4·1·22
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-9}{2*1}=\frac{4}{2}
=2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+9}{2*1}=\frac{22}{2}
=11
$