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

Solution for (1/2x)-1=2x+5 equation:

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

We move all terms to the left:

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


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

1/2x-2x-5-1=0

We multiply all the terms by the denominator


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

Wy multiply elements

-4x^2-10x-2x+1=0

We add all the numbers together, and all the variables

-4x^2-12x+1=0

a = -4; b = -12; c = +1;
Δ = b2-4ac
Δ = -122-4·(-4)·1
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{10}}{2*-4}=\frac{12-4\sqrt{10}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{10}}{2*-4}=\frac{12+4\sqrt{10}}{-8}
$