x^2-40x+31=0

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

x^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}
$