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=5Y^2-44Y+91
We move all terms to the left:
-(5Y^2-44Y+91)=0
We get rid of parentheses
-5Y^2+44Y-91=0
a = -5; b = 44; c = -91;
Δ = b2-4ac
Δ = 442-4·(-5)·(-91)
Δ = 116
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}$$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{116}=\sqrt{4*29}=\sqrt{4}*\sqrt{29}=2\sqrt{29}$$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-2\sqrt{29}}{2*-5}=\frac{-44-2\sqrt{29}}{-10} $$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+2\sqrt{29}}{2*-5}=\frac{-44+2\sqrt{29}}{-10} $
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