x^2-64x+208=0

Solution for x^2-64x+208=0 equation:

x^2-64x+208=0

a = 1; b = -64; c = +208;
Δ = b2-4ac
Δ = -642-4·1·208
Δ = 3264
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:

$\sqrt{\Delta}=\sqrt{3264}=\sqrt{64*51}=\sqrt{64}*\sqrt{51}=8\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-8\sqrt{51}}{2*1}=\frac{64-8\sqrt{51}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+8\sqrt{51}}{2*1}=\frac{64+8\sqrt{51}}{2}
$