2x=1/2x+21

Solution for 2x=1/2x+21 equation:

2x=1/2x+21

We move all terms to the left:

2x-(1/2x+21)=0


Domain of the equation: 2x+21)!=0

x∈R


We get rid of parentheses

2x-1/2x-21=0

We multiply all the terms by the denominator


2x*2x-21*2x-1=0

Wy multiply elements

4x^2-42x-1=0

a = 4; b = -42; c = -1;
Δ = b2-4ac
Δ = -422-4·4·(-1)
Δ = 1780
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:

$\sqrt{\Delta}=\sqrt{1780}=\sqrt{4*445}=\sqrt{4}*\sqrt{445}=2\sqrt{445}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{445}}{2*4}=\frac{42-2\sqrt{445}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{445}}{2*4}=\frac{42+2\sqrt{445}}{8}
$