3x=2/33x-2

Solution for 3x=2/33x-2 equation:

3x=2/33x-2

We move all terms to the left:

3x-(2/33x-2)=0


Domain of the equation: 33x-2)!=0

x∈R


We get rid of parentheses

3x-2/33x+2=0

We multiply all the terms by the denominator


3x*33x+2*33x-2=0

Wy multiply elements

99x^2+66x-2=0

a = 99; b = 66; c = -2;
Δ = b2-4ac
Δ = 662-4·99·(-2)
Δ = 5148
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:

$\sqrt{\Delta}=\sqrt{5148}=\sqrt{36*143}=\sqrt{36}*\sqrt{143}=6\sqrt{143}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(66)-6\sqrt{143}}{2*99}=\frac{-66-6\sqrt{143}}{198}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(66)+6\sqrt{143}}{2*99}=\frac{-66+6\sqrt{143}}{198}
$