5-1/3x=5/4x+2

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

5-1/3x=5/4x+2

We move all terms to the left:

5-1/3x-(5/4x+2)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 4x+2)!=0

x∈R


We get rid of parentheses

-1/3x-5/4x-2+5=0

We calculate fractions


(-4x)/12x^2+(-15x)/12x^2-2+5=0

We add all the numbers together, and all the variables

(-4x)/12x^2+(-15x)/12x^2+3=0

We multiply all the terms by the denominator


(-4x)+(-15x)+3*12x^2=0

Wy multiply elements

36x^2+(-4x)+(-15x)=0

We get rid of parentheses

36x^2-4x-15x=0

We add all the numbers together, and all the variables

36x^2-19x=0

a = 36; b = -19; c = 0;
Δ = b2-4ac
Δ = -192-4·36·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-19}{2*36}=\frac{0}{72}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+19}{2*36}=\frac{38}{72}
=19/36
$