5w(5w+8)=9

Solution for 5w(5w+8)=9 equation:

5w(5w+8)=9

We move all terms to the left:

5w(5w+8)-(9)=0

We multiply parentheses

25w^2+40w-9=0

a = 25; b = 40; c = -9;
Δ = b2-4ac
Δ = 402-4·25·(-9)
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-50}{2*25}=\frac{-90}{50}
=-1+4/5
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+50}{2*25}=\frac{10}{50}
=1/5
$