9w(w-9)-2=-7w+7(w-8)

Solution for 9w(w-9)-2=-7w+7(w-8) equation:

9w(w-9)-2=-7w+7(w-8)

We move all terms to the left:

9w(w-9)-2-(-7w+7(w-8))=0

We multiply parentheses

9w^2-81w-(-7w+7(w-8))-2=0


We calculate terms in parentheses: -(-7w+7(w-8)), so:

-7w+7(w-8)

We multiply parentheses

-7w+7w-56

We add all the numbers together, and all the variables

-56

Back to the equation:

-(-56)


We add all the numbers together, and all the variables

9w^2-81w+54=0

a = 9; b = -81; c = +54;
Δ = b2-4ac
Δ = -812-4·9·54
Δ = 4617
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:

$\sqrt{\Delta}=\sqrt{4617}=\sqrt{81*57}=\sqrt{81}*\sqrt{57}=9\sqrt{57}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-81)-9\sqrt{57}}{2*9}=\frac{81-9\sqrt{57}}{18}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-81)+9\sqrt{57}}{2*9}=\frac{81+9\sqrt{57}}{18}
$