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w(21-w)=10w
We move all terms to the left:
w(21-w)-(10w)=0
We add all the numbers together, and all the variables
w(-1w+21)-10w=0
We add all the numbers together, and all the variables
-10w+w(-1w+21)=0
We multiply parentheses
-1w^2-10w+21w=0
We add all the numbers together, and all the variables
-1w^2+11w=0
a = -1; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-1)·0
Δ = 121
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{121}=11$$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-1}=\frac{-22}{-2} =+11 $$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-1}=\frac{0}{-2} =0 $
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