a^2=-56-15a

Solution for a^2=-56-15a equation:

a^2=-56-15a

We move all terms to the left:

a^2-(-56-15a)=0

We add all the numbers together, and all the variables

a^2-(-15a-56)=0

We get rid of parentheses

a^2+15a+56=0

a = 1; b = 15; c = +56;
Δ = b2-4ac
Δ = 152-4·1·56
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-1}{2*1}=\frac{-16}{2}
=-8
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+1}{2*1}=\frac{-14}{2}
=-7
$