0=x^2-6x-31

Solution for 0=x^2-6x-31 equation:

0=x^2-6x-31

We move all terms to the left:

0-(x^2-6x-31)=0

We add all the numbers together, and all the variables

-(x^2-6x-31)=0

We get rid of parentheses

-x^2+6x+31=0

We add all the numbers together, and all the variables

-1x^2+6x+31=0

a = -1; b = 6; c = +31;
Δ = b2-4ac
Δ = 62-4·(-1)·31
Δ = 160
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-4\sqrt{10}}{2*-1}=\frac{-6-4\sqrt{10}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+4\sqrt{10}}{2*-1}=\frac{-6+4\sqrt{10}}{-2}
$