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(2w-4)(w)=68
We move all terms to the left:
(2w-4)(w)-(68)=0
We multiply parentheses
2w^2-4w-68=0
a = 2; b = -4; c = -68;
Δ = b2-4ac
Δ = -42-4·2·(-68)
Δ = 560
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}$$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{560}=\sqrt{16*35}=\sqrt{16}*\sqrt{35}=4\sqrt{35}$$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{35}}{2*2}=\frac{4-4\sqrt{35}}{4} $$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{35}}{2*2}=\frac{4+4\sqrt{35}}{4} $
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