x/3x-5=2x+6

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

x/3x-5=2x+6

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-6x^2+x-18x-15x=0

We add all the numbers together, and all the variables

-6x^2-32x=0

a = -6; b = -32; c = 0;
Δ = b2-4ac
Δ = -322-4·(-6)·0
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-32}{2*-6}=\frac{0}{-12}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+32}{2*-6}=\frac{64}{-12}
=-5+1/3
$