1/x=2x+3

Solution for 1/x=2x+3 equation:

1/x=2x+3

We move all terms to the left:

1/x-(2x+3)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

1/x-2x-3=0

We multiply all the terms by the denominator


-2x*x-3*x+1=0

We add all the numbers together, and all the variables

-3x-2x*x+1=0

Wy multiply elements

-2x^2-3x+1=0

a = -2; b = -3; c = +1;
Δ = b2-4ac
Δ = -32-4·(-2)·1
Δ = 17
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{-(-3)-\sqrt{17}}{2*-2}=\frac{3-\sqrt{17}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{17}}{2*-2}=\frac{3+\sqrt{17}}{-4}
$