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-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:We get rid of parentheses
6(w+5)
We multiply parentheses
6w+30
Back to the equation:
-(6w+30)
-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} $
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