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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x+5)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

(-2x^2)/3x^2+9x/3x^2-1=0

We multiply all the terms by the denominator


(-2x^2)+9x-1*3x^2=0

Wy multiply elements

(-2x^2)-3x^2+9x=0

We get rid of parentheses

-2x^2-3x^2+9x=0

We add all the numbers together, and all the variables

-5x^2+9x=0

a = -5; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-5)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*-5}=\frac{-18}{-10}
=1+4/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-5}=\frac{0}{-10}
=0
$