(1/2x)-1=9-2x

Solution for (1/2x)-1=9-2x equation:

(1/2x)-1=9-2x

We move all terms to the left:

(1/2x)-1-(9-2x)=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+9)-1=0

We get rid of parentheses

1/2x+2x-9-1=0

We multiply all the terms by the denominator


2x*2x-9*2x-1*2x+1=0

Wy multiply elements

4x^2-18x-2x+1=0

We add all the numbers together, and all the variables

4x^2-20x+1=0

a = 4; b = -20; c = +1;
Δ = b2-4ac
Δ = -202-4·4·1
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-8\sqrt{6}}{2*4}=\frac{20-8\sqrt{6}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+8\sqrt{6}}{2*4}=\frac{20+8\sqrt{6}}{8}
$