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=800Y-4Y^2-15000
We move all terms to the left:
-(800Y-4Y^2-15000)=0
We get rid of parentheses
4Y^2-800Y+15000=0
a = 4; b = -800; c = +15000;
Δ = b2-4ac
Δ = -8002-4·4·15000
Δ = 400000
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}$$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{400000}=\sqrt{40000*10}=\sqrt{40000}*\sqrt{10}=200\sqrt{10}$$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-800)-200\sqrt{10}}{2*4}=\frac{800-200\sqrt{10}}{8} $$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-800)+200\sqrt{10}}{2*4}=\frac{800+200\sqrt{10}}{8} $
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