1/3x=8/5x-3

Solution for 1/3x=8/5x-3 equation:

1/3x=8/5x-3

We move all terms to the left:

1/3x-(8/5x-3)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 5x-3)!=0

x∈R


We get rid of parentheses

1/3x-8/5x+3=0

We calculate fractions


5x/15x^2+(-24x)/15x^2+3=0

We multiply all the terms by the denominator


5x+(-24x)+3*15x^2=0

Wy multiply elements

45x^2+5x+(-24x)=0

We get rid of parentheses

45x^2+5x-24x=0

We add all the numbers together, and all the variables

45x^2-19x=0

a = 45; b = -19; c = 0;
Δ = b2-4ac
Δ = -192-4·45·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-19}{2*45}=\frac{0}{90}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+19}{2*45}=\frac{38}{90}
=19/45
$