4x-2/x-3=2/1

Solution for 4x-2/x-3=2/1 equation:

4x-2/x-3=2/1

We move all terms to the left:

4x-2/x-3-(2/1)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

4x-2/x-3-0=0

We add all the numbers together, and all the variables

4x-2/x-3=0

We multiply all the terms by the denominator


4x*x-3*x-2=0

We add all the numbers together, and all the variables

-3x+4x*x-2=0

Wy multiply elements

4x^2-3x-2=0

a = 4; b = -3; c = -2;
Δ = b2-4ac
Δ = -32-4·4·(-2)
Δ = 41
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{41}}{2*4}=\frac{3-\sqrt{41}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{41}}{2*4}=\frac{3+\sqrt{41}}{8}
$