-2/5x-7/15x+1/3=-48

Solution for -2/5x-7/15x+1/3=-48 equation:

-2/5x-7/15x+1/3=-48

We move all terms to the left:

-2/5x-7/15x+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

-2/5x-7/15x+48+1/3=0

We calculate fractions


75x^2/675x^2+(-270x)/675x^2+(-315x)/675x^2+48=0

We multiply all the terms by the denominator


75x^2+(-270x)+(-315x)+48*675x^2=0

Wy multiply elements

75x^2+32400x^2+(-270x)+(-315x)=0

We get rid of parentheses

75x^2+32400x^2-270x-315x=0

We add all the numbers together, and all the variables

32475x^2-585x=0

a = 32475; b = -585; c = 0;
Δ = b2-4ac
Δ = -5852-4·32475·0
Δ = 342225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{342225}=585$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-585)-585}{2*32475}=\frac{0}{64950}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-585)+585}{2*32475}=\frac{1170}{64950}
=39/2165
$