a^2-3a-6=-8a

Solution for a^2-3a-6=-8a equation:

a^2-3a-6=-8a

We move all terms to the left:

a^2-3a-6-(-8a)=0

We get rid of parentheses

a^2-3a+8a-6=0

We add all the numbers together, and all the variables

a^2+5a-6=0

a = 1; b = 5; c = -6;
Δ = b2-4ac
Δ = 52-4·1·(-6)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-7}{2*1}=\frac{-12}{2}
=-6
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+7}{2*1}=\frac{2}{2}
=1
$