X(x-14)=1

Solution for X(x-14)=1 equation:

X(X-14)=1

We move all terms to the left:

X(X-14)-(1)=0

We multiply parentheses

X^2-14X-1=0

a = 1; b = -14; c = -1;
Δ = b2-4ac
Δ = -142-4·1·(-1)
Δ = 200
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:

$\sqrt{\Delta}=\sqrt{200}=\sqrt{100*2}=\sqrt{100}*\sqrt{2}=10\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-10\sqrt{2}}{2*1}=\frac{14-10\sqrt{2}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+10\sqrt{2}}{2*1}=\frac{14+10\sqrt{2}}{2}
$