6a^2+12a+15=33

Solution for 6a^2+12a+15=33 equation:

6a^2+12a+15=33

We move all terms to the left:

6a^2+12a+15-(33)=0

We add all the numbers together, and all the variables

6a^2+12a-18=0

a = 6; b = 12; c = -18;
Δ = b2-4ac
Δ = 122-4·6·(-18)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-24}{2*6}=\frac{-36}{12}
=-3
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+24}{2*6}=\frac{12}{12}
=1
$