a*(a+4.5)=90

Solution for a*(a+4.5)=90 equation:

a(a+4.5)=90

We move all terms to the left:

a(a+4.5)-(90)=0

We multiply parentheses

a^2+4.5a-90=0

a = 1; b = 4.5; c = -90;
Δ = b2-4ac
Δ = 4.52-4·1·(-90)
Δ = 380.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4.5)-\sqrt{380.25}}{2*1}=\frac{-4.5-\sqrt{380.25}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4.5)+\sqrt{380.25}}{2*1}=\frac{-4.5+\sqrt{380.25}}{2}
$