2/5x-3=8-1/3x=5/69

Solution for 2/5x-3=8-1/3x=5/69 equation:

2/5x-3=8-1/3x=5/69

We move all terms to the left:

2/5x-3-(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

2/5x-(-1/3x+8)-3=0

We get rid of parentheses

2/5x+1/3x-8-3=0

We calculate fractions


6x/15x^2+5x/15x^2-8-3=0

We add all the numbers together, and all the variables

6x/15x^2+5x/15x^2-11=0

We multiply all the terms by the denominator


6x+5x-11*15x^2=0

We add all the numbers together, and all the variables

11x-11*15x^2=0

Wy multiply elements

-165x^2+11x=0

a = -165; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-165)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-165}=\frac{-22}{-330}
=1/15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-165}=\frac{0}{-330}
=0
$