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 = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{15}}{2*-1}=\frac{8-2\sqrt{15}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{15}}{2*-1}=\frac{8+2\sqrt{15}}{-2}
$