3/2x=9x

Solution for 3/2x=9x equation:

3/2x=9x

We move all terms to the left:

3/2x-(9x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-9x+3/2x=0

We multiply all the terms by the denominator


-9x*2x+3=0

Wy multiply elements

-18x^2+3=0

a = -18; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-18)·3
Δ = 216
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:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{6}}{2*-18}=\frac{0-6\sqrt{6}}{-36}
=-\frac{6\sqrt{6}}{-36}
=-\frac{\sqrt{6}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{6}}{2*-18}=\frac{0+6\sqrt{6}}{-36}
=\frac{6\sqrt{6}}{-36}
=\frac{\sqrt{6}}{-6}
$