2x^2-64=x

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

2x^2-64=x

We move all terms to the left:

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

We add all the numbers together, and all the variables

2x^2-1x-64=0

a = 2; b = -1; c = -64;
Δ = b2-4ac
Δ = -12-4·2·(-64)
Δ = 513
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:

$\sqrt{\Delta}=\sqrt{513}=\sqrt{9*57}=\sqrt{9}*\sqrt{57}=3\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-3\sqrt{57}}{2*2}=\frac{1-3\sqrt{57}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+3\sqrt{57}}{2*2}=\frac{1+3\sqrt{57}}{4}
$