5x-9/x=12

Solution for 5x-9/x=12 equation:

5x-9/x=12

We move all terms to the left:

5x-9/x-(12)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


5x*x-12*x-9=0

We add all the numbers together, and all the variables

-12x+5x*x-9=0

Wy multiply elements

5x^2-12x-9=0

a = 5; b = -12; c = -9;
Δ = b2-4ac
Δ = -122-4·5·(-9)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-18}{2*5}=\frac{-6}{10}
=-3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+18}{2*5}=\frac{30}{10}
=3
$