-x^2-31x-3=0

Solution for -x^2-31x-3=0 equation:

-x^2-31x-3=0

We add all the numbers together, and all the variables

-1x^2-31x-3=0

a = -1; b = -31; c = -3;
Δ = b2-4ac
Δ = -312-4·(-1)·(-3)
Δ = 949
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{-(-31)-\sqrt{949}}{2*-1}=\frac{31-\sqrt{949}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+\sqrt{949}}{2*-1}=\frac{31+\sqrt{949}}{-2}
$