2x+1/3x+13=x-3

Solution for 2x+1/3x+13=x-3 equation:

2x+1/3x+13=x-3

We move all terms to the left:

2x+1/3x+13-(x-3)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

2x+1/3x-x+3+13=0

We multiply all the terms by the denominator


2x*3x-x*3x+3*3x+13*3x+1=0

Wy multiply elements

6x^2-3x^2+9x+39x+1=0

We add all the numbers together, and all the variables

3x^2+48x+1=0

a = 3; b = 48; c = +1;
Δ = b2-4ac
Δ = 482-4·3·1
Δ = 2292
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:

$\sqrt{\Delta}=\sqrt{2292}=\sqrt{4*573}=\sqrt{4}*\sqrt{573}=2\sqrt{573}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-2\sqrt{573}}{2*3}=\frac{-48-2\sqrt{573}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+2\sqrt{573}}{2*3}=\frac{-48+2\sqrt{573}}{6}
$