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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x+5)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


6x/2x^2+(-9x)/2x^2-5+4=0

We add all the numbers together, and all the variables

6x/2x^2+(-9x)/2x^2-1=0

We multiply all the terms by the denominator


6x+(-9x)-1*2x^2=0

Wy multiply elements

-2x^2+6x+(-9x)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

-2x^2-3x=0

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