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=Y2+5Y-2
We move all terms to the left:
-(Y2+5Y-2)=0
We add all the numbers together, and all the variables
-(+Y^2+5Y-2)=0
We get rid of parentheses
-Y^2-5Y+2=0
We add all the numbers together, and all the variables
-1Y^2-5Y+2=0
a = -1; b = -5; c = +2;
Δ = b2-4ac
Δ = -52-4·(-1)·2
Δ = 33
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}$$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{33}}{2*-1}=\frac{5-\sqrt{33}}{-2} $$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{33}}{2*-1}=\frac{5+\sqrt{33}}{-2} $
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