4w-9(6-5w)w=44

Solution for 4w-9(6-5w)w=44 equation:

4w-9(6-5w)w=44

We move all terms to the left:

4w-9(6-5w)w-(44)=0

We add all the numbers together, and all the variables

4w-9(-5w+6)w-44=0

We multiply parentheses

45w^2+4w-54w-44=0

We add all the numbers together, and all the variables

45w^2-50w-44=0

a = 45; b = -50; c = -44;
Δ = b2-4ac
Δ = -502-4·45·(-44)
Δ = 10420
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:

$\sqrt{\Delta}=\sqrt{10420}=\sqrt{4*2605}=\sqrt{4}*\sqrt{2605}=2\sqrt{2605}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-2\sqrt{2605}}{2*45}=\frac{50-2\sqrt{2605}}{90}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+2\sqrt{2605}}{2*45}=\frac{50+2\sqrt{2605}}{90}
$