8/x=2x+1

Solution for 8/x=2x+1 equation:

8/x=2x+1

We move all terms to the left:

8/x-(2x+1)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

8/x-2x-1=0

We multiply all the terms by the denominator


-2x*x-1*x+8=0

We add all the numbers together, and all the variables

-1x-2x*x+8=0

Wy multiply elements

-2x^2-1x+8=0

a = -2; b = -1; c = +8;
Δ = b2-4ac
Δ = -12-4·(-2)·8
Δ = 65
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{-(-1)-\sqrt{65}}{2*-2}=\frac{1-\sqrt{65}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{65}}{2*-2}=\frac{1+\sqrt{65}}{-4}
$