5/3x-17/5=4/15x

Solution for 5/3x-17/5=4/15x equation:

5/3x-17/5=4/15x

We move all terms to the left:

5/3x-17/5-(4/15x)=0


Domain of the equation: 3x!=0

x!=0/3

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

5/3x-(+4/15x)-17/5=0

We get rid of parentheses

5/3x-4/15x-17/5=0

We calculate fractions


(-765x^2)/1125x^2+1875x/1125x^2+(-300x)/1125x^2=0

We multiply all the terms by the denominator


(-765x^2)+1875x+(-300x)=0

We get rid of parentheses

-765x^2+1875x-300x=0

We add all the numbers together, and all the variables

-765x^2+1575x=0

a = -765; b = 1575; c = 0;
Δ = b2-4ac
Δ = 15752-4·(-765)·0
Δ = 2480625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2480625}=1575$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1575)-1575}{2*-765}=\frac{-3150}{-1530}
=2+1/17
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1575)+1575}{2*-765}=\frac{0}{-1530}
=0
$