5/2x-1/3x=4

Solution for 5/2x-1/3x=4 equation:

5/2x-1/3x=4

We move all terms to the left:

5/2x-1/3x-(4)=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 calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

-24x^2+15x+(-2x)=0

We get rid of parentheses

-24x^2+15x-2x=0

We add all the numbers together, and all the variables

-24x^2+13x=0

a = -24; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-24)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*-24}=\frac{-26}{-48}
=13/24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-24}=\frac{0}{-48}
=0
$