a(a+6)=216

Solution for a(a+6)=216 equation:

a(a+6)=216

We move all terms to the left:

a(a+6)-(216)=0

We multiply parentheses

a^2+6a-216=0

a = 1; b = 6; c = -216;
Δ = b2-4ac
Δ = 62-4·1·(-216)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-30}{2*1}=\frac{-36}{2}
=-18
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+30}{2*1}=\frac{24}{2}
=12
$