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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 4x+1)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


20x/12x^2+6x/12x^2-1+4=0

We add all the numbers together, and all the variables

20x/12x^2+6x/12x^2+3=0

We multiply all the terms by the denominator


20x+6x+3*12x^2=0

We add all the numbers together, and all the variables

26x+3*12x^2=0

Wy multiply elements

36x^2+26x=0

a = 36; b = 26; c = 0;
Δ = b2-4ac
Δ = 262-4·36·0
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-26}{2*36}=\frac{-52}{72}
=-13/18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+26}{2*36}=\frac{0}{72}
=0
$