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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-12x)/375x^2+125x/375x^2+9x/375x^2-8=0

We multiply all the terms by the denominator


(-12x)+125x+9x-8*375x^2=0

We add all the numbers together, and all the variables

134x+(-12x)-8*375x^2=0

Wy multiply elements

-3000x^2+134x+(-12x)=0

We get rid of parentheses

-3000x^2+134x-12x=0

We add all the numbers together, and all the variables

-3000x^2+122x=0

a = -3000; b = 122; c = 0;
Δ = b2-4ac
Δ = 1222-4·(-3000)·0
Δ = 14884
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14884}=122$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(122)-122}{2*-3000}=\frac{-244}{-6000}
=61/1500
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(122)+122}{2*-3000}=\frac{0}{-6000}
=0
$