4/x=5/(2x)+3

Solution for 4/x=5/(2x)+3 equation:

4/x=5/(2x)+3

We move all terms to the left:

4/x-(5/(2x)+3)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x+3)!=0

x∈R


We get rid of parentheses

4/x-5/2x-3=0

We calculate fractions


8x/2x^2+(-5x)/2x^2-3=0

We multiply all the terms by the denominator


8x+(-5x)-3*2x^2=0

Wy multiply elements

-6x^2+8x+(-5x)=0

We get rid of parentheses

-6x^2+8x-5x=0

We add all the numbers together, and all the variables

-6x^2+3x=0

a = -6; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-6)·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*-6}=\frac{-6}{-12}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-6}=\frac{0}{-12}
=0
$