5/x+3/2x=4

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

5/x+3/2x=4

We move all terms to the left:

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


10x/2x^2+3x/2x^2-4=0

We multiply all the terms by the denominator


10x+3x-4*2x^2=0

We add all the numbers together, and all the variables

13x-4*2x^2=0

Wy multiply elements

-8x^2+13x=0

a = -8; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-8)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*-8}=\frac{-26}{-16}
=1+5/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-8}=\frac{0}{-16}
=0
$