2x+2=7/x-1

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

2x+2=7/x-1

We move all terms to the left:

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


Domain of the equation: x-1)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

3x+2x*x-7=0

Wy multiply elements

2x^2+3x-7=0

a = 2; b = 3; c = -7;
Δ = b2-4ac
Δ = 32-4·2·(-7)
Δ = 65
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{-(3)-\sqrt{65}}{2*2}=\frac{-3-\sqrt{65}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{65}}{2*2}=\frac{-3+\sqrt{65}}{4}
$