Y=-x2+3x+2

Solution for Y=-x2+3x+2 equation:

=-Y2+3Y+2

We move all terms to the left:

-(-Y2+3Y+2)=0

We add all the numbers together, and all the variables

-(-1Y^2+3Y+2)=0

We get rid of parentheses

1Y^2-3Y-2=0

We add all the numbers together, and all the variables

Y^2-3Y-2=0

a = 1; b = -3; c = -2;
Δ = b2-4ac
Δ = -32-4·1·(-2)
Δ = 17
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{-(-3)-\sqrt{17}}{2*1}=\frac{3-\sqrt{17}}{2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{17}}{2*1}=\frac{3+\sqrt{17}}{2}
$