5/3x-1/5=1/5x-4

Solution for 5/3x-1/5=1/5x-4 equation:

5/3x-1/5=1/5x-4

We move all terms to the left:

5/3x-1/5-(1/5x-4)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 5x-4)!=0

x∈R


We get rid of parentheses

5/3x-1/5x+4-1/5=0

We calculate fractions


625x/375x^2+(-3x)/375x^2+(-3x)/375x^2+4=0

We multiply all the terms by the denominator


625x+(-3x)+(-3x)+4*375x^2=0

Wy multiply elements

1500x^2+625x+(-3x)+(-3x)=0

We get rid of parentheses

1500x^2+625x-3x-3x=0

We add all the numbers together, and all the variables

1500x^2+619x=0

a = 1500; b = 619; c = 0;
Δ = b2-4ac
Δ = 6192-4·1500·0
Δ = 383161
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{383161}=619$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(619)-619}{2*1500}=\frac{-1238}{3000}
=-619/1500
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(619)+619}{2*1500}=\frac{0}{3000}
=0
$