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(2w-3)*w=209
We move all terms to the left:
(2w-3)*w-(209)=0
We multiply parentheses
2w^2-3w-209=0
a = 2; b = -3; c = -209;
Δ = b2-4ac
Δ = -32-4·2·(-209)
Δ = 1681
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{1681}=41$$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-41}{2*2}=\frac{-38}{4} =-9+1/2 $$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+41}{2*2}=\frac{44}{4} =11 $
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