Y=X2+8x-1

Solution for Y=X2+8x-1 equation:

=Y2+8Y-1

We move all terms to the left:

-(Y2+8Y-1)=0

We add all the numbers together, and all the variables

-(+Y^2+8Y-1)=0

We get rid of parentheses

-Y^2-8Y+1=0

We add all the numbers together, and all the variables

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

a = -1; b = -8; c = +1;
Δ = b2-4ac
Δ = -82-4·(-1)·1
Δ = 68
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{68}=\sqrt{4*17}=\sqrt{4}*\sqrt{17}=2\sqrt{17}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{17}}{2*-1}=\frac{8-2\sqrt{17}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{17}}{2*-1}=\frac{8+2\sqrt{17}}{-2}
$