-2x^2-14x+13=-23

Solution for -2x^2-14x+13=-23 equation:

-2x^2-14x+13=-23

We move all terms to the left:

-2x^2-14x+13-(-23)=0

We add all the numbers together, and all the variables

-2x^2-14x+36=0

a = -2; b = -14; c = +36;
Δ = b2-4ac
Δ = -142-4·(-2)·36
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-22}{2*-2}=\frac{-8}{-4}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+22}{2*-2}=\frac{36}{-4}
=-9
$