x^2-6x-83=5

Solution for x^2-6x-83=5 equation:

x^2-6x-83=5

We move all terms to the left:

x^2-6x-83-(5)=0

We add all the numbers together, and all the variables

x^2-6x-88=0

a = 1; b = -6; c = -88;
Δ = b2-4ac
Δ = -62-4·1·(-88)
Δ = 388
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:

$\sqrt{\Delta}=\sqrt{388}=\sqrt{4*97}=\sqrt{4}*\sqrt{97}=2\sqrt{97}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{97}}{2*1}=\frac{6-2\sqrt{97}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{97}}{2*1}=\frac{6+2\sqrt{97}}{2}
$