x^2-2x-65=5

Solution for x^2-2x-65=5 equation:

x^2-2x-65=5

We move all terms to the left:

x^2-2x-65-(5)=0

We add all the numbers together, and all the variables

x^2-2x-70=0

a = 1; b = -2; c = -70;
Δ = b2-4ac
Δ = -22-4·1·(-70)
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{-(-2)-2\sqrt{71}}{2*1}=\frac{2-2\sqrt{71}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{71}}{2*1}=\frac{2+2\sqrt{71}}{2}
$