6-8x=-3x(-2+4x)+4x

Solution for 6-8x=-3x(-2+4x)+4x equation:

6-8x=-3x(-2+4x)+4x

We move all terms to the left:

6-8x-(-3x(-2+4x)+4x)=0

We add all the numbers together, and all the variables

-8x-(-3x(4x-2)+4x)+6=0


We calculate terms in parentheses: -(-3x(4x-2)+4x), so:

-3x(4x-2)+4x

We add all the numbers together, and all the variables

4x-3x(4x-2)

We multiply parentheses

-12x^2+4x+6x

We add all the numbers together, and all the variables

-12x^2+10x

Back to the equation:

-(-12x^2+10x)


We get rid of parentheses

12x^2-10x-8x+6=0

We add all the numbers together, and all the variables

12x^2-18x+6=0

a = 12; b = -18; c = +6;
Δ = b2-4ac
Δ = -182-4·12·6
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6}{2*12}=\frac{12}{24}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6}{2*12}=\frac{24}{24}
=1
$