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=Y2-5Y-14
We move all terms to the left:
-(Y2-5Y-14)=0
We add all the numbers together, and all the variables
-(+Y^2-5Y-14)=0
We get rid of parentheses
-Y^2+5Y+14=0
We add all the numbers together, and all the variables
-1Y^2+5Y+14=0
a = -1; b = 5; c = +14;
Δ = b2-4ac
Δ = 52-4·(-1)·14
Δ = 81
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{81}=9$$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-9}{2*-1}=\frac{-14}{-2} =+7 $$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+9}{2*-1}=\frac{4}{-2} =-2 $
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