(13)/(2x)-(4)/(15)=(31)/(6x)

Solution for (13)/(2x)-(4)/(15)=(31)/(6x) equation:

(13)/(2x)-(4)/(15)=(31)/(6x)

We move all terms to the left:

(13)/(2x)-(4)/(15)-((31)/(6x))=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

13/2x-(+31/6x)-4/15=0

We get rid of parentheses

13/2x-31/6x-4/15=0

We calculate fractions


(-288x^2)/180x^2+1170x/180x^2+(-930x)/180x^2=0

We multiply all the terms by the denominator


(-288x^2)+1170x+(-930x)=0

We get rid of parentheses

-288x^2+1170x-930x=0

We add all the numbers together, and all the variables

-288x^2+240x=0

a = -288; b = 240; c = 0;
Δ = b2-4ac
Δ = 2402-4·(-288)·0
Δ = 57600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{57600}=240$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(240)-240}{2*-288}=\frac{-480}{-576}
=5/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(240)+240}{2*-288}=\frac{0}{-576}
=0
$