Y=-x2+4x+2

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Solution for Y=-x2+4x+2 equation:



=-Y2+4Y+2
We move all terms to the left:
-(-Y2+4Y+2)=0
We add all the numbers together, and all the variables
-(-1Y^2+4Y+2)=0
We get rid of parentheses
1Y^2-4Y-2=0
We add all the numbers together, and all the variables
Y^2-4Y-2=0
a = 1; b = -4; c = -2;
Δ = b2-4ac
Δ = -42-4·1·(-2)
Δ = 24
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:
$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{6}}{2*1}=\frac{4-2\sqrt{6}}{2} $
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{6}}{2*1}=\frac{4+2\sqrt{6}}{2} $

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