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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x+9)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


6x/6x^2+(-15x)/6x^2-9-4=0

We add all the numbers together, and all the variables

6x/6x^2+(-15x)/6x^2-13=0

We multiply all the terms by the denominator


6x+(-15x)-13*6x^2=0

Wy multiply elements

-78x^2+6x+(-15x)=0

We get rid of parentheses

-78x^2+6x-15x=0

We add all the numbers together, and all the variables

-78x^2-9x=0

a = -78; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·(-78)·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*-78}=\frac{0}{-156}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*-78}=\frac{18}{-156}
=-3/26
$