(1/2x)-2=6x+20

Solution for (1/2x)-2=6x+20 equation:

(1/2x)-2=6x+20

We move all terms to the left:

(1/2x)-2-(6x+20)=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)-(6x+20)-2=0

We get rid of parentheses

1/2x-6x-20-2=0

We multiply all the terms by the denominator


-6x*2x-20*2x-2*2x+1=0

Wy multiply elements

-12x^2-40x-4x+1=0

We add all the numbers together, and all the variables

-12x^2-44x+1=0

a = -12; b = -44; c = +1;
Δ = b2-4ac
Δ = -442-4·(-12)·1
Δ = 1984
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:

$\sqrt{\Delta}=\sqrt{1984}=\sqrt{64*31}=\sqrt{64}*\sqrt{31}=8\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-8\sqrt{31}}{2*-12}=\frac{44-8\sqrt{31}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+8\sqrt{31}}{2*-12}=\frac{44+8\sqrt{31}}{-24}
$