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=-7Y^2+463Y-3166
We move all terms to the left:
-(-7Y^2+463Y-3166)=0
We get rid of parentheses
7Y^2-463Y+3166=0
a = 7; b = -463; c = +3166;
Δ = b2-4ac
Δ = -4632-4·7·3166
Δ = 125721
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}$$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{125721}=\sqrt{9*13969}=\sqrt{9}*\sqrt{13969}=3\sqrt{13969}$$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-463)-3\sqrt{13969}}{2*7}=\frac{463-3\sqrt{13969}}{14} $$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-463)+3\sqrt{13969}}{2*7}=\frac{463+3\sqrt{13969}}{14} $
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