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(3w+7)w=66
We move all terms to the left:
(3w+7)w-(66)=0
We multiply parentheses
3w^2+7w-66=0
a = 3; b = 7; c = -66;
Δ = b2-4ac
Δ = 72-4·3·(-66)
Δ = 841
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}$$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{841}=29$$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-29}{2*3}=\frac{-36}{6} =-6 $$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+29}{2*3}=\frac{22}{6} =3+2/3 $
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