-3(4w-9)9w=6(w+5)

Solution for -3(4w-9)9w=6(w+5) equation:

-3(4w-9)9w=6(w+5)

We move all terms to the left:

-3(4w-9)9w-(6(w+5))=0

We multiply parentheses

-108w^2+243w-(6(w+5))=0


We calculate terms in parentheses: -(6(w+5)), so:

6(w+5)

We multiply parentheses

6w+30

Back to the equation:

-(6w+30)


We get rid of parentheses

-108w^2+243w-6w-30=0

We add all the numbers together, and all the variables

-108w^2+237w-30=0

a = -108; b = 237; c = -30;
Δ = b2-4ac
Δ = 2372-4·(-108)·(-30)
Δ = 43209
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:

$\sqrt{\Delta}=\sqrt{43209}=\sqrt{9*4801}=\sqrt{9}*\sqrt{4801}=3\sqrt{4801}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(237)-3\sqrt{4801}}{2*-108}=\frac{-237-3\sqrt{4801}}{-216}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(237)+3\sqrt{4801}}{2*-108}=\frac{-237+3\sqrt{4801}}{-216}
$