1/3x+4=3/5x+8

Solution for 1/3x+4=3/5x+8 equation:

1/3x+4=3/5x+8

We move all terms to the left:

1/3x+4-(3/5x+8)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 5x+8)!=0

x∈R


We get rid of parentheses

1/3x-3/5x-8+4=0

We calculate fractions


5x/15x^2+(-9x)/15x^2-8+4=0

We add all the numbers together, and all the variables

5x/15x^2+(-9x)/15x^2-4=0

We multiply all the terms by the denominator


5x+(-9x)-4*15x^2=0

Wy multiply elements

-60x^2+5x+(-9x)=0

We get rid of parentheses

-60x^2+5x-9x=0

We add all the numbers together, and all the variables

-60x^2-4x=0

a = -60; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-60)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*-60}=\frac{0}{-120}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-60}=\frac{8}{-120}
=-1/15
$