Y=16+-9X+x^2

Solution for Y=16+-9X+x^2 equation:

=16+-9Y+Y^2

We move all terms to the left:

-(16+-9Y+Y^2)=0

We use the square of the difference formula

-(16-9Y+Y^2)=0

We get rid of parentheses

-Y^2+9Y-16=0

We add all the numbers together, and all the variables

-1Y^2+9Y-16=0

a = -1; b = 9; c = -16;
Δ = b2-4ac
Δ = 92-4·(-1)·(-16)
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{-(9)-\sqrt{17}}{2*-1}=\frac{-9-\sqrt{17}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{17}}{2*-1}=\frac{-9+\sqrt{17}}{-2}
$