4/X-1+6/3X+1=7/3x+1

Solution for 4/X-1+6/3X+1=7/3x+1 equation:

4/X-1+6/3X+1=7/3X+1

We move all terms to the left:

4/X-1+6/3X+1-(7/3X+1)=0


Domain of the equation: X!=0

X∈R



Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R



Domain of the equation: 3X+1)!=0

X∈R


We add all the numbers together, and all the variables

4/X+6/3X-(7/3X+1)=0

We get rid of parentheses

4/X+6/3X-7/3X-1=0

We calculate fractions


12X/3X^2+(-7X+6)/3X^2-1=0

We multiply all the terms by the denominator


12X+(-7X+6)-1*3X^2=0

Wy multiply elements

-3X^2+12X+(-7X+6)=0

We get rid of parentheses

-3X^2+12X-7X+6=0

We add all the numbers together, and all the variables

-3X^2+5X+6=0

a = -3; b = 5; c = +6;
Δ = b2-4ac
Δ = 52-4·(-3)·6
Δ = 97
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{97}}{2*-3}=\frac{-5-\sqrt{97}}{-6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{97}}{2*-3}=\frac{-5+\sqrt{97}}{-6}
$