8/x=20x+9

Solution for 8/x=20x+9 equation:

8/x=20x+9

We move all terms to the left:

8/x-(20x+9)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

8/x-20x-9=0

We multiply all the terms by the denominator


-20x*x-9*x+8=0

We add all the numbers together, and all the variables

-9x-20x*x+8=0

Wy multiply elements

-20x^2-9x+8=0

a = -20; b = -9; c = +8;
Δ = b2-4ac
Δ = -92-4·(-20)·8
Δ = 721
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{-(-9)-\sqrt{721}}{2*-20}=\frac{9-\sqrt{721}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{721}}{2*-20}=\frac{9+\sqrt{721}}{-40}
$