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=5(Y-10)(Y+7)
We move all terms to the left:
-(5(Y-10)(Y+7))=0
We multiply parentheses ..
-(5(+Y^2+7Y-10Y-70))=0
We calculate terms in parentheses: -(5(+Y^2+7Y-10Y-70)), so:We get rid of parentheses
5(+Y^2+7Y-10Y-70)
We multiply parentheses
5Y^2+35Y-50Y-350
We add all the numbers together, and all the variables
5Y^2-15Y-350
Back to the equation:
-(5Y^2-15Y-350)
-5Y^2+15Y+350=0
a = -5; b = 15; c = +350;
Δ = b2-4ac
Δ = 152-4·(-5)·350
Δ = 7225
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}$$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{7225}=85$$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-85}{2*-5}=\frac{-100}{-10} =+10 $$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+85}{2*-5}=\frac{70}{-10} =-7 $
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