X=y^2-6y-16

Solution for X=y^2-6y-16 equation:

X=X^2-6X-16

We move all terms to the left:

X-(X^2-6X-16)=0

We get rid of parentheses

-X^2+X+6X+16=0

We add all the numbers together, and all the variables

-1X^2+7X+16=0

a = -1; b = 7; c = +16;
Δ = b2-4ac
Δ = 72-4·(-1)·16
Δ = 113
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{113}}{2*-1}=\frac{-7-\sqrt{113}}{-2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{113}}{2*-1}=\frac{-7+\sqrt{113}}{-2}
$