-x^2-2x+7=-17

Solution for -x^2-2x+7=-17 equation:

-x^2-2x+7=-17

We move all terms to the left:

-x^2-2x+7-(-17)=0

We add all the numbers together, and all the variables

-1x^2-2x+24=0

a = -1; b = -2; c = +24;
Δ = b2-4ac
Δ = -22-4·(-1)·24
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-10}{2*-1}=\frac{-8}{-2}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+10}{2*-1}=\frac{12}{-2}
=-6
$