5/2x+1/6=2/3x+2

Solution for 5/2x+1/6=2/3x+2 equation:

5/2x+1/6=2/3x+2

We move all terms to the left:

5/2x+1/6-(2/3x+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

5/2x-2/3x-2+1/6=0

We calculate fractions


18x^2/216x^2+540x/216x^2+(-144x)/216x^2-2=0

We multiply all the terms by the denominator


18x^2+540x+(-144x)-2*216x^2=0

Wy multiply elements

18x^2-432x^2+540x+(-144x)=0

We get rid of parentheses

18x^2-432x^2+540x-144x=0

We add all the numbers together, and all the variables

-414x^2+396x=0

a = -414; b = 396; c = 0;
Δ = b2-4ac
Δ = 3962-4·(-414)·0
Δ = 156816
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{156816}=396$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(396)-396}{2*-414}=\frac{-792}{-828}
=22/23
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(396)+396}{2*-414}=\frac{0}{-828}
=0
$