3x=51/2x

Solution for 3x=51/2x equation:

3x=51/2x

We move all terms to the left:

3x-(51/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3x-(+51/2x)=0

We get rid of parentheses

3x-51/2x=0

We multiply all the terms by the denominator


3x*2x-51=0

Wy multiply elements

6x^2-51=0

a = 6; b = 0; c = -51;
Δ = b2-4ac
Δ = 02-4·6·(-51)
Δ = 1224
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:

$\sqrt{\Delta}=\sqrt{1224}=\sqrt{36*34}=\sqrt{36}*\sqrt{34}=6\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{34}}{2*6}=\frac{0-6\sqrt{34}}{12}
=-\frac{6\sqrt{34}}{12}
=-\frac{\sqrt{34}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{34}}{2*6}=\frac{0+6\sqrt{34}}{12}
=\frac{6\sqrt{34}}{12}
=\frac{\sqrt{34}}{2}
$