3a^2+18a=81

Solution for 3a^2+18a=81 equation:

3a^2+18a=81

We move all terms to the left:

3a^2+18a-(81)=0

a = 3; b = 18; c = -81;
Δ = b2-4ac
Δ = 182-4·3·(-81)
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{-(18)-36}{2*3}=\frac{-54}{6}
=-9
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+36}{2*3}=\frac{18}{6}
=3
$