a^2-12=-3a

Solution for a^2-12=-3a equation:

a^2-12=-3a

We move all terms to the left:

a^2-12-(-3a)=0

We get rid of parentheses

a^2+3a-12=0

a = 1; b = 3; c = -12;
Δ = b2-4ac
Δ = 32-4·1·(-12)
Δ = 57
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{57}}{2*1}=\frac{-3-\sqrt{57}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{57}}{2*1}=\frac{-3+\sqrt{57}}{2}
$