3*2x^2-8^2=x

Solution for 3*2x^2-8^2=x equation:

3*2x^2-8^2=x

We move all terms to the left:

3*2x^2-8^2-(x)=0

We add all the numbers together, and all the variables

-1x+3*2x^2-64=0

Wy multiply elements

6x^2-1x-64=0

a = 6; b = -1; c = -64;
Δ = b2-4ac
Δ = -12-4·6·(-64)
Δ = 1537
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{1537}}{2*6}=\frac{1-\sqrt{1537}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{1537}}{2*6}=\frac{1+\sqrt{1537}}{12}
$