6x-2=-2(1/2-3x)

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

6x-2=-2(1/2-3x)

We move all terms to the left:

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


Domain of the equation: 2-3x))!=0

We move all terms containing x to the left, all other terms to the right

-3x))!=-2

x!=-2/1

x!=-2

x∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


6x*2))-(-2(-3x+1-2*2))=0

We add all the numbers together, and all the variables

6x*2))-(-2(-3x-3))=0

We add all the numbers together, and all the variables

-3x+6x*2))-(-2(=0

Wy multiply elements

12x^2-3x=0

a = 12; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·12·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*12}=\frac{0}{24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*12}=\frac{6}{24}
=1/4
$