4/2x+1/6=8/3x-2

Solution for 4/2x+1/6=8/3x-2 equation:

4/2x+1/6=8/3x-2

We move all terms to the left:

4/2x+1/6-(8/3x-2)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



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

x∈R


We get rid of parentheses

4/2x-8/3x+2+1/6=0

We calculate fractions


18x^2/216x^2+432x/216x^2+(-576x)/216x^2+2=0

We multiply all the terms by the denominator


18x^2+432x+(-576x)+2*216x^2=0

Wy multiply elements

18x^2+432x^2+432x+(-576x)=0

We get rid of parentheses

18x^2+432x^2+432x-576x=0

We add all the numbers together, and all the variables

450x^2-144x=0

a = 450; b = -144; c = 0;
Δ = b2-4ac
Δ = -1442-4·450·0
Δ = 20736
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{20736}=144$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-144}{2*450}=\frac{0}{900}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+144}{2*450}=\frac{288}{900}
=8/25
$