6/5x+19/5+1/3x=103/15

Solution for 6/5x+19/5+1/3x=103/15 equation:

6/5x+19/5+1/3x=103/15

We move all terms to the left:

6/5x+19/5+1/3x-(103/15)=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+1/3x+19/5-(+103/15)=0

We get rid of parentheses

6/5x+1/3x+19/5-103/15=0

We calculate fractions


(-23175x^2)/5625x^2+270x/5625x^2+1875x/5625x^2+855x/5625x^2=0

We multiply all the terms by the denominator


(-23175x^2)+270x+1875x+855x=0

We add all the numbers together, and all the variables

(-23175x^2)+3000x=0

We get rid of parentheses

-23175x^2+3000x=0

a = -23175; b = 3000; c = 0;
Δ = b2-4ac
Δ = 30002-4·(-23175)·0
Δ = 9000000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9000000}=3000$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3000)-3000}{2*-23175}=\frac{-6000}{-46350}
=40/309
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3000)+3000}{2*-23175}=\frac{0}{-46350}
=0
$