4x^2-2x=64

Solution for 4x^2-2x=64 equation:

4x^2-2x=64

We move all terms to the left:

4x^2-2x-(64)=0

a = 4; b = -2; c = -64;
Δ = b2-4ac
Δ = -22-4·4·(-64)
Δ = 1028
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:

$\sqrt{\Delta}=\sqrt{1028}=\sqrt{4*257}=\sqrt{4}*\sqrt{257}=2\sqrt{257}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{257}}{2*4}=\frac{2-2\sqrt{257}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{257}}{2*4}=\frac{2+2\sqrt{257}}{8}
$