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=-9Y^2+14Y+1
We move all terms to the left:
-(-9Y^2+14Y+1)=0
We get rid of parentheses
9Y^2-14Y-1=0
a = 9; b = -14; c = -1;
Δ = b2-4ac
Δ = -142-4·9·(-1)
Δ = 232
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}$$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{232}=\sqrt{4*58}=\sqrt{4}*\sqrt{58}=2\sqrt{58}$$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{58}}{2*9}=\frac{14-2\sqrt{58}}{18} $$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{58}}{2*9}=\frac{14+2\sqrt{58}}{18} $
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