3x+1=2/3x+4

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

3x+1=2/3x+4

We move all terms to the left:

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


Domain of the equation: 3x+4)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


3x*3x-4*3x+1*3x-2=0

Wy multiply elements

9x^2-12x+3x-2=0

We add all the numbers together, and all the variables

9x^2-9x-2=0

a = 9; b = -9; c = -2;
Δ = b2-4ac
Δ = -92-4·9·(-2)
Δ = 153
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:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{17}}{2*9}=\frac{9-3\sqrt{17}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{17}}{2*9}=\frac{9+3\sqrt{17}}{18}
$