w(2w-8)=9

Solution for w(2w-8)=9 equation:

w(2w-8)=9

We move all terms to the left:

w(2w-8)-(9)=0

We multiply parentheses

2w^2-8w-9=0

a = 2; b = -8; c = -9;
Δ = b2-4ac
Δ = -82-4·2·(-9)
Δ = 136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{34}}{2*2}=\frac{8-2\sqrt{34}}{4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{34}}{2*2}=\frac{8+2\sqrt{34}}{4}
$