12/2x-13=12/9x+4

Solution for 12/2x-13=12/9x+4 equation:

12/2x-13=12/9x+4

We move all terms to the left:

12/2x-13-(12/9x+4)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 9x+4)!=0

x∈R


We get rid of parentheses

12/2x-12/9x-4-13=0

We calculate fractions


108x/18x^2+(-24x)/18x^2-4-13=0

We add all the numbers together, and all the variables

108x/18x^2+(-24x)/18x^2-17=0

We multiply all the terms by the denominator


108x+(-24x)-17*18x^2=0

Wy multiply elements

-306x^2+108x+(-24x)=0

We get rid of parentheses

-306x^2+108x-24x=0

We add all the numbers together, and all the variables

-306x^2+84x=0

a = -306; b = 84; c = 0;
Δ = b2-4ac
Δ = 842-4·(-306)·0
Δ = 7056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7056}=84$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-84}{2*-306}=\frac{-168}{-612}
=14/51
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+84}{2*-306}=\frac{0}{-612}
=0
$