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=Y2-12Y+31
We move all terms to the left:
-(Y2-12Y+31)=0
We add all the numbers together, and all the variables
-(+Y^2-12Y+31)=0
We get rid of parentheses
-Y^2+12Y-31=0
We add all the numbers together, and all the variables
-1Y^2+12Y-31=0
a = -1; b = 12; c = -31;
Δ = b2-4ac
Δ = 122-4·(-1)·(-31)
Δ = 20
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}$$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{5}}{2*-1}=\frac{-12-2\sqrt{5}}{-2} $$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{5}}{2*-1}=\frac{-12+2\sqrt{5}}{-2} $
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