X=x^2-12x+31

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

X=X^2-12X+31

We move all terms to the left:

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

We get rid of parentheses

-X^2+X+12X-31=0

We add all the numbers together, and all the variables

-1X^2+13X-31=0

a = -1; b = 13; c = -31;
Δ = b2-4ac
Δ = 132-4·(-1)·(-31)
Δ = 45
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:

$\sqrt{\Delta}=\sqrt{45}=\sqrt{9*5}=\sqrt{9}*\sqrt{5}=3\sqrt{5}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-3\sqrt{5}}{2*-1}=\frac{-13-3\sqrt{5}}{-2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+3\sqrt{5}}{2*-1}=\frac{-13+3\sqrt{5}}{-2}
$