x/3x+7+2x=9x-1

Solution for x/3x+7+2x=9x-1 equation:

x/3x+7+2x=9x-1

We move all terms to the left:

x/3x+7+2x-(9x-1)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

2x+x/3x-(9x-1)+7=0

We get rid of parentheses

2x+x/3x-9x+1+7=0

We multiply all the terms by the denominator


2x*3x+x-9x*3x+1*3x+7*3x=0

We add all the numbers together, and all the variables

x+2x*3x-9x*3x+1*3x+7*3x=0

Wy multiply elements

6x^2-27x^2+x+3x+21x=0

We add all the numbers together, and all the variables

-21x^2+25x=0

a = -21; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·(-21)·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-25}{2*-21}=\frac{-50}{-42}
=1+4/21
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*-21}=\frac{0}{-42}
=0
$