1-8x-x^2=0

Solution for 1-8x-x^2=0 equation:

1-8x-x^2=0

We add all the numbers together, and all the variables

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

The end solution:

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