9/2x=4-3/x

Solution for 9/2x=4-3/x equation:

9/2x=4-3/x

We move all terms to the left:

9/2x-(4-3/x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

9/2x-(-3/x+4)=0

We get rid of parentheses

9/2x+3/x-4=0

We calculate fractions


9x/2x^2+6x/2x^2-4=0

We multiply all the terms by the denominator


9x+6x-4*2x^2=0

We add all the numbers together, and all the variables

15x-4*2x^2=0

Wy multiply elements

-8x^2+15x=0

a = -8; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·(-8)·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15}{2*-8}=\frac{-30}{-16}
=1+7/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*-8}=\frac{0}{-16}
=0
$