x^2-14x=218

Solution for x^2-14x=218 equation:

x^2-14x=218

We move all terms to the left:

x^2-14x-(218)=0

a = 1; b = -14; c = -218;
Δ = b2-4ac
Δ = -142-4·1·(-218)
Δ = 1068
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:

$\sqrt{\Delta}=\sqrt{1068}=\sqrt{4*267}=\sqrt{4}*\sqrt{267}=2\sqrt{267}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{267}}{2*1}=\frac{14-2\sqrt{267}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{267}}{2*1}=\frac{14+2\sqrt{267}}{2}
$