a^2+a-12=10

Solution for a^2+a-12=10 equation:

a^2+a-12=10

We move all terms to the left:

a^2+a-12-(10)=0

We add all the numbers together, and all the variables

a^2+a-22=0

a = 1; b = 1; c = -22;
Δ = b2-4ac
Δ = 12-4·1·(-22)
Δ = 89
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{-(1)-\sqrt{89}}{2*1}=\frac{-1-\sqrt{89}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{89}}{2*1}=\frac{-1+\sqrt{89}}{2}
$