4/3x=2/5x-1

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

4/3x=2/5x-1

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 5x-1)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


20x+(-6x)+1*15x^2=0

Wy multiply elements

15x^2+20x+(-6x)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

15x^2+14x=0

a = 15; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·15·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*15}=\frac{-28}{30}
=-14/15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*15}=\frac{0}{30}
=0
$