x^2-31x+31=0

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

x^2-31x+31=0

a = 1; b = -31; c = +31;
Δ = b2-4ac
Δ = -312-4·1·31
Δ = 837
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:

$\sqrt{\Delta}=\sqrt{837}=\sqrt{9*93}=\sqrt{9}*\sqrt{93}=3\sqrt{93}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-3\sqrt{93}}{2*1}=\frac{31-3\sqrt{93}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+3\sqrt{93}}{2*1}=\frac{31+3\sqrt{93}}{2}
$