2/x1+3/x=2

Solution for 2/x1+3/x=2 equation:

2/x1+3/x=2

We move all terms to the left:

2/x1+3/x-(2)=0


Domain of the equation: x1!=0

x^1!=0/

x^1!=√0

x!=0

x∈R



Domain of the equation: x!=0

x∈R


We calculate fractions


2x/x^2+3x/x^2-2=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-2x^2+5x=0

a = -2; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-2)·0
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{-(5)-5}{2*-2}=\frac{-10}{-4}
=2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-2}=\frac{0}{-4}
=0
$