x^2-14x=31

Solution for x^2-14x=31 equation:

x^2-14x=31

We move all terms to the left:

x^2-14x-(31)=0

a = 1; b = -14; c = -31;
Δ = b2-4ac
Δ = -142-4·1·(-31)
Δ = 320
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:

$\sqrt{\Delta}=\sqrt{320}=\sqrt{64*5}=\sqrt{64}*\sqrt{5}=8\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-8\sqrt{5}}{2*1}=\frac{14-8\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+8\sqrt{5}}{2*1}=\frac{14+8\sqrt{5}}{2}
$