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=Y^2+21Y+18
We move all terms to the left:
-(Y^2+21Y+18)=0
We get rid of parentheses
-Y^2-21Y-18=0
We add all the numbers together, and all the variables
-1Y^2-21Y-18=0
a = -1; b = -21; c = -18;
Δ = b2-4ac
Δ = -212-4·(-1)·(-18)
Δ = 369
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}$$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{369}=\sqrt{9*41}=\sqrt{9}*\sqrt{41}=3\sqrt{41}$$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-3\sqrt{41}}{2*-1}=\frac{21-3\sqrt{41}}{-2} $$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+3\sqrt{41}}{2*-1}=\frac{21+3\sqrt{41}}{-2} $
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