3a^2+15a-18=3

Solution for 3a^2+15a-18=3 equation:

3a^2+15a-18=3

We move all terms to the left:

3a^2+15a-18-(3)=0

We add all the numbers together, and all the variables

3a^2+15a-21=0

a = 3; b = 15; c = -21;
Δ = b2-4ac
Δ = 152-4·3·(-21)
Δ = 477
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{477}=\sqrt{9*53}=\sqrt{9}*\sqrt{53}=3\sqrt{53}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3\sqrt{53}}{2*3}=\frac{-15-3\sqrt{53}}{6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3\sqrt{53}}{2*3}=\frac{-15+3\sqrt{53}}{6}
$