5/2x-1-9/3x-2=0

Solution for 5/2x-1-9/3x-2=0 equation:

5/2x-1-9/3x-2=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

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

We calculate fractions


15x/6x^2+(-18x)/6x^2-3=0

We multiply all the terms by the denominator


15x+(-18x)-3*6x^2=0

Wy multiply elements

-18x^2+15x+(-18x)=0

We get rid of parentheses

-18x^2+15x-18x=0

We add all the numbers together, and all the variables

-18x^2-3x=0

a = -18; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-18)·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*-18}=\frac{0}{-36}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-18}=\frac{6}{-36}
=-1/6
$