a2+13a=12

Solution for a2+13a=12 equation:

a2+13a=12

We move all terms to the left:

a2+13a-(12)=0

We add all the numbers together, and all the variables

a^2+13a-12=0

a = 1; b = 13; c = -12;
Δ = b2-4ac
Δ = 132-4·1·(-12)
Δ = 217
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{-(13)-\sqrt{217}}{2*1}=\frac{-13-\sqrt{217}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{217}}{2*1}=\frac{-13+\sqrt{217}}{2}
$