x^2-31x=2

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

x^2-31x=2

We move all terms to the left:

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

a = 1; b = -31; c = -2;
Δ = b2-4ac
Δ = -312-4·1·(-2)
Δ = 969
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-\sqrt{969}}{2*1}=\frac{31-\sqrt{969}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+\sqrt{969}}{2*1}=\frac{31+\sqrt{969}}{2}
$