4x-1/2x=22

Solution for 4x-1/2x=22 equation:

4x-1/2x=22

We move all terms to the left:

4x-1/2x-(22)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


4x*2x-22*2x-1=0

Wy multiply elements

8x^2-44x-1=0

a = 8; b = -44; c = -1;
Δ = b2-4ac
Δ = -442-4·8·(-1)
Δ = 1968
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:

$\sqrt{\Delta}=\sqrt{1968}=\sqrt{16*123}=\sqrt{16}*\sqrt{123}=4\sqrt{123}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-4\sqrt{123}}{2*8}=\frac{44-4\sqrt{123}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+4\sqrt{123}}{2*8}=\frac{44+4\sqrt{123}}{16}
$