225x=1/2x

Solution for 225x=1/2x equation:

225x=1/2x

We move all terms to the left:

225x-(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

225x-(+1/2x)=0

We get rid of parentheses

225x-1/2x=0

We multiply all the terms by the denominator


225x*2x-1=0

Wy multiply elements

450x^2-1=0

a = 450; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·450·(-1)
Δ = 1800
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:

$\sqrt{\Delta}=\sqrt{1800}=\sqrt{900*2}=\sqrt{900}*\sqrt{2}=30\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30\sqrt{2}}{2*450}=\frac{0-30\sqrt{2}}{900}
=-\frac{30\sqrt{2}}{900}
=-\frac{\sqrt{2}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30\sqrt{2}}{2*450}=\frac{0+30\sqrt{2}}{900}
=\frac{30\sqrt{2}}{900}
=\frac{\sqrt{2}}{30}
$