x2-14x-82=2

Solution for x2-14x-82=2 equation:

x2-14x-82=2

We move all terms to the left:

x2-14x-82-(2)=0

We add all the numbers together, and all the variables

x^2-14x-84=0

a = 1; b = -14; c = -84;
Δ = b2-4ac
Δ = -142-4·1·(-84)
Δ = 532
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:

$\sqrt{\Delta}=\sqrt{532}=\sqrt{4*133}=\sqrt{4}*\sqrt{133}=2\sqrt{133}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{133}}{2*1}=\frac{14-2\sqrt{133}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{133}}{2*1}=\frac{14+2\sqrt{133}}{2}
$