3x+2/x-5=2

Solution for 3x+2/x-5=2 equation:

3x+2/x-5=2

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

3x+2/x-7=0

We multiply all the terms by the denominator


3x*x-7*x+2=0

We add all the numbers together, and all the variables

-7x+3x*x+2=0

Wy multiply elements

3x^2-7x+2=0

a = 3; b = -7; c = +2;
Δ = b2-4ac
Δ = -72-4·3·2
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-5}{2*3}=\frac{2}{6}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+5}{2*3}=\frac{12}{6}
=2
$