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=-10Y^2-40Y-9
We move all terms to the left:
-(-10Y^2-40Y-9)=0
We get rid of parentheses
10Y^2+40Y+9=0
a = 10; b = 40; c = +9;
Δ = b2-4ac
Δ = 402-4·10·9
Δ = 1240
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}$$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1240}=\sqrt{4*310}=\sqrt{4}*\sqrt{310}=2\sqrt{310}$$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-2\sqrt{310}}{2*10}=\frac{-40-2\sqrt{310}}{20} $$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+2\sqrt{310}}{2*10}=\frac{-40+2\sqrt{310}}{20} $
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