X2+8x=-1

Solution for X2+8x=-1 equation:

X2+8X=-1

We move all terms to the left:

X2+8X-(-1)=0

We add all the numbers together, and all the variables

X^2+8X+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:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

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