6x/x^2-36=0

Solution for 6x/x^2-36=0 equation:

6x/x^2-36=0


Domain of the equation: x^2!=0

x^2!=0/

x^2!=√0

x!=0

x∈R


We multiply all the terms by the denominator


6x-36*x^2=0

We add all the numbers together, and all the variables

-36x^2+6x=0

a = -36; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-36)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*-36}=\frac{-12}{-72}
=1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-36}=\frac{0}{-72}
=0
$