x/3x=5x-8/5

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

x/3x=5x-8/5

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


-5x+5x/15x+24x/15x=0

We multiply all the terms by the denominator


-5x*15x+5x+24x=0

We add all the numbers together, and all the variables

29x-5x*15x=0

Wy multiply elements

-75x^2+29x=0

a = -75; b = 29; c = 0;
Δ = b2-4ac
Δ = 292-4·(-75)·0
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-29}{2*-75}=\frac{-58}{-150}
=29/75
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+29}{2*-75}=\frac{0}{-150}
=0
$