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(25-y)y=100
We move all terms to the left:
(25-y)y-(100)=0
We add all the numbers together, and all the variables
(-1y+25)y-100=0
We multiply parentheses
-1y^2+25y-100=0
a = -1; b = 25; c = -100;
Δ = b2-4ac
Δ = 252-4·(-1)·(-100)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{225}=15$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-15}{2*-1}=\frac{-40}{-2} =+20 $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+15}{2*-1}=\frac{-10}{-2} =+5 $
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