2x+3=1/3x-4

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

2x+3=1/3x-4

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

6x^2+12x+9x-1=0

We add all the numbers together, and all the variables

6x^2+21x-1=0

a = 6; b = 21; c = -1;
Δ = b2-4ac
Δ = 212-4·6·(-1)
Δ = 465
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{-(21)-\sqrt{465}}{2*6}=\frac{-21-\sqrt{465}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{465}}{2*6}=\frac{-21+\sqrt{465}}{12}
$