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=-16Y^2+189Y+79
We move all terms to the left:
-(-16Y^2+189Y+79)=0
We get rid of parentheses
16Y^2-189Y-79=0
a = 16; b = -189; c = -79;
Δ = b2-4ac
Δ = -1892-4·16·(-79)
Δ = 40777
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}$$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{40777}=\sqrt{121*337}=\sqrt{121}*\sqrt{337}=11\sqrt{337}$$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-189)-11\sqrt{337}}{2*16}=\frac{189-11\sqrt{337}}{32} $$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-189)+11\sqrt{337}}{2*16}=\frac{189+11\sqrt{337}}{32} $
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