(9)/(4x)-(5)/(6)=-(13)/(12x)

Solution for (9)/(4x)-(5)/(6)=-(13)/(12x) equation:

(9)/(4x)-(5)/(6)=-(13)/(12x)

We move all terms to the left:

(9)/(4x)-(5)/(6)-(-(13)/(12x))=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 12x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

9/4x+13/12x-5/6=0

We calculate fractions


(-240x^2)/1728x^2+3888x/1728x^2+1872x/1728x^2=0

We multiply all the terms by the denominator


(-240x^2)+3888x+1872x=0

We add all the numbers together, and all the variables

(-240x^2)+5760x=0

We get rid of parentheses

-240x^2+5760x=0

a = -240; b = 5760; c = 0;
Δ = b2-4ac
Δ = 57602-4·(-240)·0
Δ = 33177600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{33177600}=5760$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5760)-5760}{2*-240}=\frac{-11520}{-480}
=+24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5760)+5760}{2*-240}=\frac{0}{-480}
=0
$