X2-66x+1=0

Solution for X2-66x+1=0 equation:

X2-66X+1=0

We add all the numbers together, and all the variables

X^2-66X+1=0

a = 1; b = -66; c = +1;
Δ = b2-4ac
Δ = -662-4·1·1
Δ = 4352
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:

$\sqrt{\Delta}=\sqrt{4352}=\sqrt{256*17}=\sqrt{256}*\sqrt{17}=16\sqrt{17}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-16\sqrt{17}}{2*1}=\frac{66-16\sqrt{17}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+16\sqrt{17}}{2*1}=\frac{66+16\sqrt{17}}{2}
$