2/33x-6=4x-2

Solution for 2/33x-6=4x-2 equation:

2/33x-6=4x-2

We move all terms to the left:

2/33x-6-(4x-2)=0


Domain of the equation: 33x!=0

x!=0/33

x!=0

x∈R


We get rid of parentheses

2/33x-4x+2-6=0

We multiply all the terms by the denominator


-4x*33x+2*33x-6*33x+2=0

Wy multiply elements

-132x^2+66x-198x+2=0

We add all the numbers together, and all the variables

-132x^2-132x+2=0

a = -132; b = -132; c = +2;
Δ = b2-4ac
Δ = -1322-4·(-132)·2
Δ = 18480
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:

$\sqrt{\Delta}=\sqrt{18480}=\sqrt{16*1155}=\sqrt{16}*\sqrt{1155}=4\sqrt{1155}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-132)-4\sqrt{1155}}{2*-132}=\frac{132-4\sqrt{1155}}{-264}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-132)+4\sqrt{1155}}{2*-132}=\frac{132+4\sqrt{1155}}{-264}
$