a^2-52=-9a

Solution for a^2-52=-9a equation:

a^2-52=-9a

We move all terms to the left:

a^2-52-(-9a)=0

We get rid of parentheses

a^2+9a-52=0

a = 1; b = 9; c = -52;
Δ = b2-4ac
Δ = 92-4·1·(-52)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-17}{2*1}=\frac{-26}{2}
=-13
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+17}{2*1}=\frac{8}{2}
=4
$