8x=16x-32/2x-1

Solution for 8x=16x-32/2x-1 equation:

8x=16x-32/2x-1

We move all terms to the left:

8x-(16x-32/2x-1)=0


Domain of the equation: 2x-1)!=0

x∈R


We get rid of parentheses

8x-16x+32/2x+1=0

We multiply all the terms by the denominator


8x*2x-16x*2x+1*2x+32=0

Wy multiply elements

16x^2-32x^2+2x+32=0

We add all the numbers together, and all the variables

-16x^2+2x+32=0

a = -16; b = 2; c = +32;
Δ = b2-4ac
Δ = 22-4·(-16)·32
Δ = 2052
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:

$\sqrt{\Delta}=\sqrt{2052}=\sqrt{36*57}=\sqrt{36}*\sqrt{57}=6\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-6\sqrt{57}}{2*-16}=\frac{-2-6\sqrt{57}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+6\sqrt{57}}{2*-16}=\frac{-2+6\sqrt{57}}{-32}
$