8^x-2/32x=16

Solution for 8^x-2/32x=16 equation:

8^x-2/32x=16

We move all terms to the left:

8^x-2/32x-(16)=0


Domain of the equation: 32x!=0

x!=0/32

x!=0

x∈R


We multiply all the terms by the denominator


8^x*32x-16*32x-2=0

Wy multiply elements

256x^2-512x-2=0

a = 256; b = -512; c = -2;
Δ = b2-4ac
Δ = -5122-4·256·(-2)
Δ = 264192
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:

$\sqrt{\Delta}=\sqrt{264192}=\sqrt{1024*258}=\sqrt{1024}*\sqrt{258}=32\sqrt{258}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-512)-32\sqrt{258}}{2*256}=\frac{512-32\sqrt{258}}{512}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-512)+32\sqrt{258}}{2*256}=\frac{512+32\sqrt{258}}{512}
$