2(2x+1)8x-6/3=0

Solution for 2(2x+1)8x-6/3=0 equation:

2(2x+1)8x-6/3=0

We add all the numbers together, and all the variables

2(2x+1)8x-2=0

We multiply parentheses

32x^2+16x-2=0

a = 32; b = 16; c = -2;
Δ = b2-4ac
Δ = 162-4·32·(-2)
Δ = 512
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:

$\sqrt{\Delta}=\sqrt{512}=\sqrt{256*2}=\sqrt{256}*\sqrt{2}=16\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16\sqrt{2}}{2*32}=\frac{-16-16\sqrt{2}}{64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16\sqrt{2}}{2*32}=\frac{-16+16\sqrt{2}}{64}
$