1.5/x+2x=4

Solution for 1.5/x+2x=4 equation:

1.5/x+2x=4

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

2x+1.5/x-4=0

We multiply all the terms by the denominator


2x*x-4*x+1.5=0

We add all the numbers together, and all the variables

-4x+2x*x+1.5=0

Wy multiply elements

2x^2-4x+1.5=0

a = 2; b = -4; c = +1.5;
Δ = b2-4ac
Δ = -42-4·2·1.5
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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