-2x-(6.7x-8)=-2/3x+4

Solution for -2x-(6.7x-8)=-2/3x+4 equation:

-2x-(6.7x-8)=-2/3x+4

We move all terms to the left:

-2x-(6.7x-8)-(-2/3x+4)=0


Domain of the equation: 3x+4)!=0

x∈R


We get rid of parentheses

-2x-6.7x+2/3x+8-4=0

We multiply all the terms by the denominator


-2x*3x-(6.7x)*3x+8*3x-4*3x+2=0

We add all the numbers together, and all the variables

-2x*3x-(+6.7x)*3x+8*3x-4*3x+2=0

We multiply parentheses

-18x^2-2x*3x+8*3x-4*3x+2=0

Wy multiply elements

-18x^2-6x^2+24x-12x+2=0

We add all the numbers together, and all the variables

-24x^2+12x+2=0

a = -24; b = 12; c = +2;
Δ = b2-4ac
Δ = 122-4·(-24)·2
Δ = 336
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:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{21}}{2*-24}=\frac{-12-4\sqrt{21}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{21}}{2*-24}=\frac{-12+4\sqrt{21}}{-48}
$