4/4x+3/x=2

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

4/4x+3/x=2

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: x!=0

x∈R


We calculate fractions


4x/4x^2+12x/4x^2-2=0

We multiply all the terms by the denominator


4x+12x-2*4x^2=0

We add all the numbers together, and all the variables

16x-2*4x^2=0

Wy multiply elements

-8x^2+16x=0

a = -8; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·(-8)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*-8}=\frac{-32}{-16}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*-8}=\frac{0}{-16}
=0
$