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=5Y^2+30Y+7
We move all terms to the left:
-(5Y^2+30Y+7)=0
We get rid of parentheses
-5Y^2-30Y-7=0
a = -5; b = -30; c = -7;
Δ = b2-4ac
Δ = -302-4·(-5)·(-7)
Δ = 760
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}$$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{760}=\sqrt{4*190}=\sqrt{4}*\sqrt{190}=2\sqrt{190}$$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{190}}{2*-5}=\frac{30-2\sqrt{190}}{-10} $$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{190}}{2*-5}=\frac{30+2\sqrt{190}}{-10} $
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