X^2-64x+12=0

Solution for X^2-64x+12=0 equation:

X^2-64X+12=0

a = 1; b = -64; c = +12;
Δ = b2-4ac
Δ = -642-4·1·12
Δ = 4048
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:

$\sqrt{\Delta}=\sqrt{4048}=\sqrt{16*253}=\sqrt{16}*\sqrt{253}=4\sqrt{253}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-4\sqrt{253}}{2*1}=\frac{64-4\sqrt{253}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+4\sqrt{253}}{2*1}=\frac{64+4\sqrt{253}}{2}
$