4x^2-64=x

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

4x^2-64=x

We move all terms to the left:

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

We add all the numbers together, and all the variables

4x^2-1x-64=0

a = 4; b = -1; c = -64;
Δ = b2-4ac
Δ = -12-4·4·(-64)
Δ = 1025
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:

$\sqrt{\Delta}=\sqrt{1025}=\sqrt{25*41}=\sqrt{25}*\sqrt{41}=5\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-5\sqrt{41}}{2*4}=\frac{1-5\sqrt{41}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+5\sqrt{41}}{2*4}=\frac{1+5\sqrt{41}}{8}
$