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=1000Y^2+1100Y-2.5
We move all terms to the left:
-(1000Y^2+1100Y-2.5)=0
We get rid of parentheses
-1000Y^2-1100Y+2.5=0
a = -1000; b = -1100; c = +2.5;
Δ = b2-4ac
Δ = -11002-4·(-1000)·2.5
Δ = 1220000
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}$$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1220000}=\sqrt{10000*122}=\sqrt{10000}*\sqrt{122}=100\sqrt{122}$$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1100)-100\sqrt{122}}{2*-1000}=\frac{1100-100\sqrt{122}}{-2000} $$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1100)+100\sqrt{122}}{2*-1000}=\frac{1100+100\sqrt{122}}{-2000} $
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