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

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

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

We move all terms to the left:

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


Domain of the equation: 1x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


21x/3x^2+(-5x+1)/3x^2-2=0

We multiply all the terms by the denominator


21x+(-5x+1)-2*3x^2=0

Wy multiply elements

-6x^2+21x+(-5x+1)=0

We get rid of parentheses

-6x^2+21x-5x+1=0

We add all the numbers together, and all the variables

-6x^2+16x+1=0

a = -6; b = 16; c = +1;
Δ = b2-4ac
Δ = 162-4·(-6)·1
Δ = 280
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:

$\sqrt{\Delta}=\sqrt{280}=\sqrt{4*70}=\sqrt{4}*\sqrt{70}=2\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{70}}{2*-6}=\frac{-16-2\sqrt{70}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{70}}{2*-6}=\frac{-16+2\sqrt{70}}{-12}
$