5/x+9/2x=4

Solution for 5/x+9/2x=4 equation:

5/x+9/2x=4

We move all terms to the left:

5/x+9/2x-(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+9x/2x^2-4=0

We multiply all the terms by the denominator


10x+9x-4*2x^2=0

We add all the numbers together, and all the variables

19x-4*2x^2=0

Wy multiply elements

-8x^2+19x=0

a = -8; b = 19; c = 0;
Δ = b2-4ac
Δ = 192-4·(-8)·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-19}{2*-8}=\frac{-38}{-16}
=2+3/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+19}{2*-8}=\frac{0}{-16}
=0
$