-x^2-x=-18

Solution for -x^2-x=-18 equation:

-x^2-x=-18

We move all terms to the left:

-x^2-x-(-18)=0

We add all the numbers together, and all the variables

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

a = -1; b = -1; c = +18;
Δ = b2-4ac
Δ = -12-4·(-1)·18
Δ = 73
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{73}}{2*-1}=\frac{1-\sqrt{73}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{73}}{2*-1}=\frac{1+\sqrt{73}}{-2}
$