1/3x+2/3x+5=7x-1

Solution for 1/3x+2/3x+5=7x-1 equation:

1/3x+2/3x+5=7x-1

We move all terms to the left:

1/3x+2/3x+5-(7x-1)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

1/3x+2/3x-7x+1+5=0

We multiply all the terms by the denominator


-7x*3x+1*3x+5*3x+1+2=0

We add all the numbers together, and all the variables

-7x*3x+1*3x+5*3x+3=0

Wy multiply elements

-21x^2+3x+15x+3=0

We add all the numbers together, and all the variables

-21x^2+18x+3=0

a = -21; b = 18; c = +3;
Δ = b2-4ac
Δ = 182-4·(-21)·3
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-24}{2*-21}=\frac{-42}{-42}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+24}{2*-21}=\frac{6}{-42}
=-1/7
$