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3w^2-8w-171=0
a = 3; b = -8; c = -171;
Δ = b2-4ac
Δ = -82-4·3·(-171)
Δ = 2116
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{2116}=46$$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-46}{2*3}=\frac{-38}{6} =-6+1/3 $$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+46}{2*3}=\frac{54}{6} =9 $
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