51/2x-2=2x

Solution for 51/2x-2=2x equation:

51/2x-2=2x

We move all terms to the left:

51/2x-2-(2x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-2x+51/2x-2=0

We multiply all the terms by the denominator


-2x*2x-2*2x+51=0

Wy multiply elements

-4x^2-4x+51=0

a = -4; b = -4; c = +51;
Δ = b2-4ac
Δ = -42-4·(-4)·51
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{-(-4)-8\sqrt{13}}{2*-4}=\frac{4-8\sqrt{13}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+8\sqrt{13}}{2*-4}=\frac{4+8\sqrt{13}}{-8}
$