1/x=2x+5

Solution for 1/x=2x+5 equation:

1/x=2x+5

We move all terms to the left:

1/x-(2x+5)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

1/x-2x-5=0

We multiply all the terms by the denominator


-2x*x-5*x+1=0

We add all the numbers together, and all the variables

-5x-2x*x+1=0

Wy multiply elements

-2x^2-5x+1=0

a = -2; b = -5; c = +1;
Δ = b2-4ac
Δ = -52-4·(-2)·1
Δ = 33
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{-(-5)-\sqrt{33}}{2*-2}=\frac{5-\sqrt{33}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{33}}{2*-2}=\frac{5+\sqrt{33}}{-4}
$