4x+4=1/212x

Solution for 4x+4=1/212x equation:

4x+4=1/212x

We move all terms to the left:

4x+4-(1/212x)=0


Domain of the equation: 212x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4x-(+1/212x)+4=0

We get rid of parentheses

4x-1/212x+4=0

We multiply all the terms by the denominator


4x*212x+4*212x-1=0

Wy multiply elements

848x^2+848x-1=0

a = 848; b = 848; c = -1;
Δ = b2-4ac
Δ = 8482-4·848·(-1)
Δ = 722496
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:

$\sqrt{\Delta}=\sqrt{722496}=\sqrt{64*11289}=\sqrt{64}*\sqrt{11289}=8\sqrt{11289}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(848)-8\sqrt{11289}}{2*848}=\frac{-848-8\sqrt{11289}}{1696}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(848)+8\sqrt{11289}}{2*848}=\frac{-848+8\sqrt{11289}}{1696}
$