8/5x=8-2/15x

Solution for 8/5x=8-2/15x equation:

8/5x=8-2/15x

We move all terms to the left:

8/5x-(8-2/15x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 15x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

8/5x+2/15x-8=0

We calculate fractions


120x/75x^2+10x/75x^2-8=0

We multiply all the terms by the denominator


120x+10x-8*75x^2=0

We add all the numbers together, and all the variables

130x-8*75x^2=0

Wy multiply elements

-600x^2+130x=0

a = -600; b = 130; c = 0;
Δ = b2-4ac
Δ = 1302-4·(-600)·0
Δ = 16900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16900}=130$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(130)-130}{2*-600}=\frac{-260}{-1200}
=13/60
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(130)+130}{2*-600}=\frac{0}{-1200}
=0
$