153x=5*1/2x

Solution for 153x=5*1/2x equation:

153x=5*1/2x

We move all terms to the left:

153x-(5*1/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

153x-(+5*1/2x)=0

We get rid of parentheses

153x-5*1/2x=0

We multiply all the terms by the denominator


153x*2x-5*1=0

We add all the numbers together, and all the variables

153x*2x-5=0

Wy multiply elements

306x^2-5=0

a = 306; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·306·(-5)
Δ = 6120
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:

$\sqrt{\Delta}=\sqrt{6120}=\sqrt{36*170}=\sqrt{36}*\sqrt{170}=6\sqrt{170}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{170}}{2*306}=\frac{0-6\sqrt{170}}{612}
=-\frac{6\sqrt{170}}{612}
=-\frac{\sqrt{170}}{102}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{170}}{2*306}=\frac{0+6\sqrt{170}}{612}
=\frac{6\sqrt{170}}{612}
=\frac{\sqrt{170}}{102}
$