Y=-x2+10x-9

Solution for Y=-x2+10x-9 equation:

=-Y2+10Y-9

We move all terms to the left:

-(-Y2+10Y-9)=0

We add all the numbers together, and all the variables

-(-1Y^2+10Y-9)=0

We get rid of parentheses

1Y^2-10Y+9=0

We add all the numbers together, and all the variables

Y^2-10Y+9=0

a = 1; b = -10; c = +9;
Δ = b2-4ac
Δ = -102-4·1·9
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-8}{2*1}=\frac{2}{2}
=1
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+8}{2*1}=\frac{18}{2}
=9
$