8x-6+2=2x(4-6x)

Solution for 8x-6+2=2x(4-6x) equation:

8x-6+2=2x(4-6x)

We move all terms to the left:

8x-6+2-(2x(4-6x))=0

We add all the numbers together, and all the variables

8x-(2x(-6x+4))-6+2=0

We add all the numbers together, and all the variables

8x-(2x(-6x+4))-4=0


We calculate terms in parentheses: -(2x(-6x+4)), so:

2x(-6x+4)

We multiply parentheses

-12x^2+8x

Back to the equation:

-(-12x^2+8x)


We get rid of parentheses

12x^2-8x+8x-4=0

We add all the numbers together, and all the variables

12x^2-4=0

a = 12; b = 0; c = -4;
Δ = b2-4ac
Δ = 02-4·12·(-4)
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{3}}{2*12}=\frac{0-8\sqrt{3}}{24}
=-\frac{8\sqrt{3}}{24}
=-\frac{\sqrt{3}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{3}}{2*12}=\frac{0+8\sqrt{3}}{24}
=\frac{8\sqrt{3}}{24}
=\frac{\sqrt{3}}{3}
$