-3/5x-2/15x-+1/3=-48

Solution for -3/5x-2/15x-+1/3=-48 equation:

-3/5x-2/15x-+1/3=-48

We move all terms to the left:

-3/5x-2/15x-+1/3-(-48)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 15x!=0

x!=0/15

x!=0

x∈R


We add all the numbers together, and all the variables

-3/5x-2/15x-48+1/3=0

We calculate fractions


75x^2/675x^2+(-405x)/675x^2+(-90x)/675x^2-48=0

We multiply all the terms by the denominator


75x^2+(-405x)+(-90x)-48*675x^2=0

Wy multiply elements

75x^2-32400x^2+(-405x)+(-90x)=0

We get rid of parentheses

75x^2-32400x^2-405x-90x=0

We add all the numbers together, and all the variables

-32325x^2-495x=0

a = -32325; b = -495; c = 0;
Δ = b2-4ac
Δ = -4952-4·(-32325)·0
Δ = 245025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{245025}=495$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-495)-495}{2*-32325}=\frac{0}{-64650}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-495)+495}{2*-32325}=\frac{990}{-64650}
=-33/2155
$