1/3x-6=4/5x+8

Solution for 1/3x-6=4/5x+8 equation:

1/3x-6=4/5x+8

We move all terms to the left:

1/3x-6-(4/5x+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-4/5x-8-6=0

We calculate fractions


5x/15x^2+(-12x)/15x^2-8-6=0

We add all the numbers together, and all the variables

5x/15x^2+(-12x)/15x^2-14=0

We multiply all the terms by the denominator


5x+(-12x)-14*15x^2=0

Wy multiply elements

-210x^2+5x+(-12x)=0

We get rid of parentheses

-210x^2+5x-12x=0

We add all the numbers together, and all the variables

-210x^2-7x=0

a = -210; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·(-210)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*-210}=\frac{0}{-420}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*-210}=\frac{14}{-420}
=-1/30
$