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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

-120x^2+(5x+8)+(-9x)=0

We get rid of parentheses

-120x^2+5x-9x+8=0

We add all the numbers together, and all the variables

-120x^2-4x+8=0

a = -120; b = -4; c = +8;
Δ = b2-4ac
Δ = -42-4·(-120)·8
Δ = 3856
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3856}=\sqrt{16*241}=\sqrt{16}*\sqrt{241}=4\sqrt{241}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{241}}{2*-120}=\frac{4-4\sqrt{241}}{-240}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{241}}{2*-120}=\frac{4+4\sqrt{241}}{-240}
$