2/x+6/(x+1)=7

Solution for 2/x+6/(x+1)=7 equation:

2/x+6/(x+1)=7

We move all terms to the left:

2/x+6/(x+1)-(7)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: (x+1)!=0

We move all terms containing x to the left, all other terms to the right

x!=-1

x∈R


We calculate fractions


(2x+2)/(x^2+x)+6x/(x^2+x)-7=0

We multiply all the terms by the denominator


(2x+2)+6x-7*(x^2+x)=0

We add all the numbers together, and all the variables

6x+(2x+2)-7*(x^2+x)=0

We multiply parentheses

-7x^2+6x+(2x+2)-7x=0

We get rid of parentheses

-7x^2+6x+2x-7x+2=0

We add all the numbers together, and all the variables

-7x^2+x+2=0

a = -7; b = 1; c = +2;
Δ = b2-4ac
Δ = 12-4·(-7)·2
Δ = 57
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{-(1)-\sqrt{57}}{2*-7}=\frac{-1-\sqrt{57}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{57}}{2*-7}=\frac{-1+\sqrt{57}}{-14}
$