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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 4x+5)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


12x/4x^2+(-9x)/4x^2-5+3=0

We add all the numbers together, and all the variables

12x/4x^2+(-9x)/4x^2-2=0

We multiply all the terms by the denominator


12x+(-9x)-2*4x^2=0

Wy multiply elements

-8x^2+12x+(-9x)=0

We get rid of parentheses

-8x^2+12x-9x=0

We add all the numbers together, and all the variables

-8x^2+3x=0

a = -8; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-8)·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*-8}=\frac{-6}{-16}
=3/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-8}=\frac{0}{-16}
=0
$