(3/5x)-(8/15x)=3

Solution for (3/5x)-(8/15x)=3 equation:

(3/5x)-(8/15x)=3

We move all terms to the left:

(3/5x)-(8/15x)-(3)=0


Domain of the equation: 5x)!=0

x!=0/1

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

(+3/5x)-(+8/15x)-3=0

We get rid of parentheses

3/5x-8/15x-3=0

We calculate fractions


45x/75x^2+(-40x)/75x^2-3=0

We multiply all the terms by the denominator


45x+(-40x)-3*75x^2=0

Wy multiply elements

-225x^2+45x+(-40x)=0

We get rid of parentheses

-225x^2+45x-40x=0

We add all the numbers together, and all the variables

-225x^2+5x=0

a = -225; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-225)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-225}=\frac{-10}{-450}
=1/45
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-225}=\frac{0}{-450}
=0
$