-x^2-23x-126=0

Solution for -x^2-23x-126=0 equation:

-x^2-23x-126=0

We add all the numbers together, and all the variables

-1x^2-23x-126=0

a = -1; b = -23; c = -126;
Δ = b2-4ac
Δ = -232-4·(-1)·(-126)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-5}{2*-1}=\frac{18}{-2}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+5}{2*-1}=\frac{28}{-2}
=-14
$