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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


20x/15x^2+6x/15x^2-4+1=0

We add all the numbers together, and all the variables

20x/15x^2+6x/15x^2-3=0

We multiply all the terms by the denominator


20x+6x-3*15x^2=0

We add all the numbers together, and all the variables

26x-3*15x^2=0

Wy multiply elements

-45x^2+26x=0

a = -45; b = 26; c = 0;
Δ = b2-4ac
Δ = 262-4·(-45)·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*-45}=\frac{-52}{-90}
=26/45
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+26}{2*-45}=\frac{0}{-90}
=0
$