X^2-14x-11=11

Solution for X^2-14x-11=11 equation:

X^2-14X-11=11

We move all terms to the left:

X^2-14X-11-(11)=0

We add all the numbers together, and all the variables

X^2-14X-22=0

a = 1; b = -14; c = -22;
Δ = b2-4ac
Δ = -142-4·1·(-22)
Δ = 284
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:

$\sqrt{\Delta}=\sqrt{284}=\sqrt{4*71}=\sqrt{4}*\sqrt{71}=2\sqrt{71}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{71}}{2*1}=\frac{14-2\sqrt{71}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{71}}{2*1}=\frac{14+2\sqrt{71}}{2}
$