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=-12Y^2+180Y+63
We move all terms to the left:
-(-12Y^2+180Y+63)=0
We get rid of parentheses
12Y^2-180Y-63=0
a = 12; b = -180; c = -63;
Δ = b2-4ac
Δ = -1802-4·12·(-63)
Δ = 35424
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}$$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{35424}=\sqrt{144*246}=\sqrt{144}*\sqrt{246}=12\sqrt{246}$$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-12\sqrt{246}}{2*12}=\frac{180-12\sqrt{246}}{24} $$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+12\sqrt{246}}{2*12}=\frac{180+12\sqrt{246}}{24} $
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