-x^2-8x+18=0

Solution for -x^2-8x+18=0 equation:

-x^2-8x+18=0

We add all the numbers together, and all the variables

-1x^2-8x+18=0

a = -1; b = -8; c = +18;
Δ = b2-4ac
Δ = -82-4·(-1)·18
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{34}}{2*-1}=\frac{8-2\sqrt{34}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{34}}{2*-1}=\frac{8+2\sqrt{34}}{-2}
$