x2-66x+1=66

Solution for x2-66x+1=66 equation:

x2-66x+1=66

We move all terms to the left:

x2-66x+1-(66)=0

We add all the numbers together, and all the variables

x^2-66x-65=0

a = 1; b = -66; c = -65;
Δ = b2-4ac
Δ = -662-4·1·(-65)
Δ = 4616
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:

$\sqrt{\Delta}=\sqrt{4616}=\sqrt{4*1154}=\sqrt{4}*\sqrt{1154}=2\sqrt{1154}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-2\sqrt{1154}}{2*1}=\frac{66-2\sqrt{1154}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+2\sqrt{1154}}{2*1}=\frac{66+2\sqrt{1154}}{2}
$