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w(2w-10)=1500
We move all terms to the left:
w(2w-10)-(1500)=0
We multiply parentheses
2w^2-10w-1500=0
a = 2; b = -10; c = -1500;
Δ = b2-4ac
Δ = -102-4·2·(-1500)
Δ = 12100
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{12100}=110$$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-110}{2*2}=\frac{-100}{4} =-25 $$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+110}{2*2}=\frac{120}{4} =30 $
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