a(2a+8)=90

Solution for a(2a+8)=90 equation:

a(2a+8)=90

We move all terms to the left:

a(2a+8)-(90)=0

We multiply parentheses

2a^2+8a-90=0

a = 2; b = 8; c = -90;
Δ = b2-4ac
Δ = 82-4·2·(-90)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-28}{2*2}=\frac{-36}{4}
=-9
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+28}{2*2}=\frac{20}{4}
=5
$