x2+9x-31=-6

Solution for x2+9x-31=-6 equation:

x2+9x-31=-6

We move all terms to the left:

x2+9x-31-(-6)=0

We add all the numbers together, and all the variables

x^2+9x-25=0

a = 1; b = 9; c = -25;
Δ = b2-4ac
Δ = 92-4·1·(-25)
Δ = 181
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{-(9)-\sqrt{181}}{2*1}=\frac{-9-\sqrt{181}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{181}}{2*1}=\frac{-9+\sqrt{181}}{2}
$