2x+6=3+5/3x

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

2x+6=3+5/3x

We move all terms to the left:

2x+6-(3+5/3x)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2x-(5/3x+3)+6=0

We get rid of parentheses

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

We multiply all the terms by the denominator


2x*3x-3*3x+6*3x-5=0

Wy multiply elements

6x^2-9x+18x-5=0

We add all the numbers together, and all the variables

6x^2+9x-5=0

a = 6; b = 9; c = -5;
Δ = b2-4ac
Δ = 92-4·6·(-5)
Δ = 201
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{201}}{2*6}=\frac{-9-\sqrt{201}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{201}}{2*6}=\frac{-9+\sqrt{201}}{12}
$