12a^2+24a=15

Solution for 12a^2+24a=15 equation:

12a^2+24a=15

We move all terms to the left:

12a^2+24a-(15)=0

a = 12; b = 24; c = -15;
Δ = b2-4ac
Δ = 242-4·12·(-15)
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-36}{2*12}=\frac{-60}{24}
=-2+1/2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+36}{2*12}=\frac{12}{24}
=1/2
$