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

Solution for 4x/x+2-3/2x=0 equation:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We calculate fractions


8x^2/2x^2+(-3x)/2x^2+2=0

We multiply all the terms by the denominator


8x^2+(-3x)+2*2x^2=0

Wy multiply elements

8x^2+4x^2+(-3x)=0

We get rid of parentheses

8x^2+4x^2-3x=0

We add all the numbers together, and all the variables

12x^2-3x=0

a = 12; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·12·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*12}=\frac{0}{24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*12}=\frac{6}{24}
=1/4
$