8x-16/8x=16

Solution for 8x-16/8x=16 equation:

8x-16/8x=16

We move all terms to the left:

8x-16/8x-(16)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We multiply all the terms by the denominator


8x*8x-16*8x-16=0

Wy multiply elements

64x^2-128x-16=0

a = 64; b = -128; c = -16;
Δ = b2-4ac
Δ = -1282-4·64·(-16)
Δ = 20480
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:

$\sqrt{\Delta}=\sqrt{20480}=\sqrt{4096*5}=\sqrt{4096}*\sqrt{5}=64\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-128)-64\sqrt{5}}{2*64}=\frac{128-64\sqrt{5}}{128}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-128)+64\sqrt{5}}{2*64}=\frac{128+64\sqrt{5}}{128}
$