11/x-8x=11

Solution for 11/x-8x=11 equation:

11/x-8x=11

We move all terms to the left:

11/x-8x-(11)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-8x+11/x-11=0

We multiply all the terms by the denominator


-8x*x-11*x+11=0

We add all the numbers together, and all the variables

-11x-8x*x+11=0

Wy multiply elements

-8x^2-11x+11=0

a = -8; b = -11; c = +11;
Δ = b2-4ac
Δ = -112-4·(-8)·11
Δ = 473
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-\sqrt{473}}{2*-8}=\frac{11-\sqrt{473}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{473}}{2*-8}=\frac{11+\sqrt{473}}{-16}
$