0=x^2-40x+31

Solution for 0=x^2-40x+31 equation:

0=x^2-40x+31

We move all terms to the left:

0-(x^2-40x+31)=0

We add all the numbers together, and all the variables

-(x^2-40x+31)=0

We get rid of parentheses

-x^2+40x-31=0

We add all the numbers together, and all the variables

-1x^2+40x-31=0

a = -1; b = 40; c = -31;
Δ = b2-4ac
Δ = 402-4·(-1)·(-31)
Δ = 1476
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:

$\sqrt{\Delta}=\sqrt{1476}=\sqrt{36*41}=\sqrt{36}*\sqrt{41}=6\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-6\sqrt{41}}{2*-1}=\frac{-40-6\sqrt{41}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+6\sqrt{41}}{2*-1}=\frac{-40+6\sqrt{41}}{-2}
$