3+2/x=4x

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

3+2/x=4x

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


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}
$