-x^2+8x+1=6

Solution for -x^2+8x+1=6 equation:

-x^2+8x+1=6

We move all terms to the left:

-x^2+8x+1-(6)=0

We add all the numbers together, and all the variables

-1x^2+8x-5=0

a = -1; b = 8; c = -5;
Δ = b2-4ac
Δ = 82-4·(-1)·(-5)
Δ = 44
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:

$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{11}}{2*-1}=\frac{-8-2\sqrt{11}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{11}}{2*-1}=\frac{-8+2\sqrt{11}}{-2}
$