2x+3/x-1=7

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

2x+3/x-1=7

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

2x+3/x-8=0

We multiply all the terms by the denominator


2x*x-8*x+3=0

We add all the numbers together, and all the variables

-8x+2x*x+3=0

Wy multiply elements

2x^2-8x+3=0

a = 2; b = -8; c = +3;
Δ = b2-4ac
Δ = -82-4·2·3
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{10}}{2*2}=\frac{8-2\sqrt{10}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{10}}{2*2}=\frac{8+2\sqrt{10}}{4}
$