8x+9/x-11=10

Solution for 8x+9/x-11=10 equation:

8x+9/x-11=10

We move all terms to the left:

8x+9/x-11-(10)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

8x+9/x-21=0

We multiply all the terms by the denominator


8x*x-21*x+9=0

We add all the numbers together, and all the variables

-21x+8x*x+9=0

Wy multiply elements

8x^2-21x+9=0

a = 8; b = -21; c = +9;
Δ = b2-4ac
Δ = -212-4·8·9
Δ = 153
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-3\sqrt{17}}{2*8}=\frac{21-3\sqrt{17}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+3\sqrt{17}}{2*8}=\frac{21+3\sqrt{17}}{16}
$