6/11x+9/x=1

Solution for 6/11x+9/x=1 equation:

6/11x+9/x=1

We move all terms to the left:

6/11x+9/x-(1)=0


Domain of the equation: 11x!=0

x!=0/11

x!=0

x∈R



Domain of the equation: x!=0

x∈R


We calculate fractions


6x/11x^2+99x/11x^2-1=0

We multiply all the terms by the denominator


6x+99x-1*11x^2=0

We add all the numbers together, and all the variables

105x-1*11x^2=0

Wy multiply elements

-11x^2+105x=0

a = -11; b = 105; c = 0;
Δ = b2-4ac
Δ = 1052-4·(-11)·0
Δ = 11025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11025}=105$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(105)-105}{2*-11}=\frac{-210}{-22}
=9+6/11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(105)+105}{2*-11}=\frac{0}{-22}
=0
$