(-7+9w)w=5

Solution for (-7+9w)w=5 equation:

(-7+9w)w=5

We move all terms to the left:

(-7+9w)w-(5)=0

We add all the numbers together, and all the variables

(9w-7)w-5=0

We multiply parentheses

9w^2-7w-5=0

a = 9; b = -7; c = -5;
Δ = b2-4ac
Δ = -72-4·9·(-5)
Δ = 229
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{229}}{2*9}=\frac{7-\sqrt{229}}{18}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{229}}{2*9}=\frac{7+\sqrt{229}}{18}
$