15x=3/2x

Solution for 15x=3/2x equation:

15x=3/2x

We move all terms to the left:

15x-(3/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

15x-(+3/2x)=0

We get rid of parentheses

15x-3/2x=0

We multiply all the terms by the denominator


15x*2x-3=0

Wy multiply elements

30x^2-3=0

a = 30; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·30·(-3)
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*30}=\frac{0-6\sqrt{10}}{60}
=-\frac{6\sqrt{10}}{60}
=-\frac{\sqrt{10}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{10}}{2*30}=\frac{0+6\sqrt{10}}{60}
=\frac{6\sqrt{10}}{60}
=\frac{\sqrt{10}}{10}
$