X^2-68x+1024=0

Solution for X^2-68x+1024=0 equation:

X^2-68X+1024=0

a = 1; b = -68; c = +1024;
Δ = b2-4ac
Δ = -682-4·1·1024
Δ = 528
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:

$\sqrt{\Delta}=\sqrt{528}=\sqrt{16*33}=\sqrt{16}*\sqrt{33}=4\sqrt{33}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-68)-4\sqrt{33}}{2*1}=\frac{68-4\sqrt{33}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-68)+4\sqrt{33}}{2*1}=\frac{68+4\sqrt{33}}{2}
$