0=x^2-12x+31

Solution for 0=x^2-12x+31 equation:

0=x^2-12x+31

We move all terms to the left:

0-(x^2-12x+31)=0

We add all the numbers together, and all the variables

-(x^2-12x+31)=0

We get rid of parentheses

-x^2+12x-31=0

We add all the numbers together, and all the variables

-1x^2+12x-31=0

a = -1; b = 12; c = -31;
Δ = b2-4ac
Δ = 122-4·(-1)·(-31)
Δ = 20
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:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{5}}{2*-1}=\frac{-12-2\sqrt{5}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{5}}{2*-1}=\frac{-12+2\sqrt{5}}{-2}
$