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100=w(2w-1)
We move all terms to the left:
100-(w(2w-1))=0
We calculate terms in parentheses: -(w(2w-1)), so:We get rid of parentheses
w(2w-1)
We multiply parentheses
2w^2-1w
Back to the equation:
-(2w^2-1w)
-2w^2+1w+100=0
We add all the numbers together, and all the variables
-2w^2+w+100=0
a = -2; b = 1; c = +100;
Δ = b2-4ac
Δ = 12-4·(-2)·100
Δ = 801
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}$$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{801}=\sqrt{9*89}=\sqrt{9}*\sqrt{89}=3\sqrt{89}$$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-3\sqrt{89}}{2*-2}=\frac{-1-3\sqrt{89}}{-4} $$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+3\sqrt{89}}{2*-2}=\frac{-1+3\sqrt{89}}{-4} $
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