x^2-66x+1024=0

Solution for x^2-66x+1024=0 equation:

x^2-66x+1024=0

a = 1; b = -66; c = +1024;
Δ = b2-4ac
Δ = -662-4·1·1024
Δ = 260
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:

$\sqrt{\Delta}=\sqrt{260}=\sqrt{4*65}=\sqrt{4}*\sqrt{65}=2\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-2\sqrt{65}}{2*1}=\frac{66-2\sqrt{65}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+2\sqrt{65}}{2*1}=\frac{66+2\sqrt{65}}{2}
$