6/5x+4/3x=19/15

Solution for 6/5x+4/3x=19/15 equation:

6/5x+4/3x=19/15

We move all terms to the left:

6/5x+4/3x-(19/15)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

6/5x+4/3x-(+19/15)=0

We get rid of parentheses

6/5x+4/3x-19/15=0

We calculate fractions


(-855x^2)/225x^2+270x/225x^2+300x/225x^2=0

We multiply all the terms by the denominator


(-855x^2)+270x+300x=0

We add all the numbers together, and all the variables

(-855x^2)+570x=0

We get rid of parentheses

-855x^2+570x=0

a = -855; b = 570; c = 0;
Δ = b2-4ac
Δ = 5702-4·(-855)·0
Δ = 324900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324900}=570$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(570)-570}{2*-855}=\frac{-1140}{-1710}
=2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(570)+570}{2*-855}=\frac{0}{-1710}
=0
$