5/x-2/3x=171/3

Solution for 5/x-2/3x=171/3 equation:

5/x-2/3x=171/3

We move all terms to the left:

5/x-2/3x-(171/3)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

5/x-2/3x-57=0

We calculate fractions


15x/3x^2+(-2x)/3x^2-57=0

We multiply all the terms by the denominator


15x+(-2x)-57*3x^2=0

Wy multiply elements

-171x^2+15x+(-2x)=0

We get rid of parentheses

-171x^2+15x-2x=0

We add all the numbers together, and all the variables

-171x^2+13x=0

a = -171; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-171)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*-171}=\frac{-26}{-342}
=13/171
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-171}=\frac{0}{-342}
=0
$