-4+9(3+5w)w=9

Solution for -4+9(3+5w)w=9 equation:

-4+9(3+5w)w=9

We move all terms to the left:

-4+9(3+5w)w-(9)=0

We add all the numbers together, and all the variables

9(5w+3)w-4-9=0

We add all the numbers together, and all the variables

9(5w+3)w-13=0

We multiply parentheses

45w^2+27w-13=0

a = 45; b = 27; c = -13;
Δ = b2-4ac
Δ = 272-4·45·(-13)
Δ = 3069
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:

$\sqrt{\Delta}=\sqrt{3069}=\sqrt{9*341}=\sqrt{9}*\sqrt{341}=3\sqrt{341}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-3\sqrt{341}}{2*45}=\frac{-27-3\sqrt{341}}{90}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+3\sqrt{341}}{2*45}=\frac{-27+3\sqrt{341}}{90}
$