-2/5x-8/15x+1/3=-54

Solution for -2/5x-8/15x+1/3=-54 equation:

-2/5x-8/15x+1/3=-54

We move all terms to the left:

-2/5x-8/15x+1/3-(-54)=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-8/15x+54+1/3=0

We calculate fractions


75x^2/675x^2+(-270x)/675x^2+(-360x)/675x^2+54=0

We multiply all the terms by the denominator


75x^2+(-270x)+(-360x)+54*675x^2=0

Wy multiply elements

75x^2+36450x^2+(-270x)+(-360x)=0

We get rid of parentheses

75x^2+36450x^2-270x-360x=0

We add all the numbers together, and all the variables

36525x^2-630x=0

a = 36525; b = -630; c = 0;
Δ = b2-4ac
Δ = -6302-4·36525·0
Δ = 396900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{396900}=630$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-630)-630}{2*36525}=\frac{0}{73050}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-630)+630}{2*36525}=\frac{1260}{73050}
=42/2435
$