1/2x=45x

Solution for 1/2x=45x equation:

1/2x=45x

We move all terms to the left:

1/2x-(45x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-45x+1/2x=0

We multiply all the terms by the denominator


-45x*2x+1=0

Wy multiply elements

-90x^2+1=0

a = -90; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-90)·1
Δ = 360
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:

$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{10}}{2*-90}=\frac{0-6\sqrt{10}}{-180}
=-\frac{6\sqrt{10}}{-180}
=-\frac{\sqrt{10}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{10}}{2*-90}=\frac{0+6\sqrt{10}}{-180}
=\frac{6\sqrt{10}}{-180}
=\frac{\sqrt{10}}{-30}
$