5/X+3=2/4x-9

Solution for 5/X+3=2/4x-9 equation:

5/X+3=2/4X-9

We move all terms to the left:

5/X+3-(2/4X-9)=0


Domain of the equation: X!=0

X∈R



Domain of the equation: 4X-9)!=0

X∈R


We get rid of parentheses

5/X-2/4X+9+3=0

We calculate fractions


20X/4X^2+(-2X)/4X^2+9+3=0

We add all the numbers together, and all the variables

20X/4X^2+(-2X)/4X^2+12=0

We multiply all the terms by the denominator


20X+(-2X)+12*4X^2=0

Wy multiply elements

48X^2+20X+(-2X)=0

We get rid of parentheses

48X^2+20X-2X=0

We add all the numbers together, and all the variables

48X^2+18X=0

a = 48; b = 18; c = 0;
Δ = b2-4ac
Δ = 182-4·48·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18}{2*48}=\frac{-36}{96}
=-3/8
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18}{2*48}=\frac{0}{96}
=0
$