Y=8+6x+x2

Solution for Y=8+6x+x2 equation:

=8+6Y+Y2

We move all terms to the left:

-(8+6Y+Y2)=0

We add all the numbers together, and all the variables

-(+6Y+Y^2+8)=0

We get rid of parentheses

-Y^2-6Y-8=0

We add all the numbers together, and all the variables

-1Y^2-6Y-8=0

a = -1; b = -6; c = -8;
Δ = b2-4ac
Δ = -62-4·(-1)·(-8)
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2}{2*-1}=\frac{4}{-2}
=-2
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2}{2*-1}=\frac{8}{-2}
=-4
$