12x-8/2xx=4

Solution for 12x-8/2xx=4 equation:

12x-8/2xx=4

We move all terms to the left:

12x-8/2xx-(4)=0


Domain of the equation: 2xx!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


12x*2xx-4*2xx-8=0

Wy multiply elements

24x^2-8x-8=0

a = 24; b = -8; c = -8;
Δ = b2-4ac
Δ = -82-4·24·(-8)
Δ = 832
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:

$\sqrt{\Delta}=\sqrt{832}=\sqrt{64*13}=\sqrt{64}*\sqrt{13}=8\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8\sqrt{13}}{2*24}=\frac{8-8\sqrt{13}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8\sqrt{13}}{2*24}=\frac{8+8\sqrt{13}}{48}
$