6x/x^2+9=1

Solution for 6x/x^2+9=1 equation:

6x/x^2+9=1

We move all terms to the left:

6x/x^2+9-(1)=0


Domain of the equation: x^2!=0

x^2!=0/

x^2!=√0

x!=0

x∈R


We add all the numbers together, and all the variables

6x/x^2+8=0

We multiply all the terms by the denominator


6x+8*x^2=0

We add all the numbers together, and all the variables

8x^2+6x=0

a = 8; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·8·0
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*8}=\frac{-12}{16}
=-3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*8}=\frac{0}{16}
=0
$