3x=1/2x*15.

Solution for 3x=1/2x*15. equation:

3x=1/2x*15.

We move all terms to the left:

3x-(1/2x*15.)=0


Domain of the equation: 2x*15.)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3x-(+1/2x*15.)=0

We get rid of parentheses

3x-1/2x*15.=0

We multiply all the terms by the denominator


3x*2x*15.-1=0

Wy multiply elements

90x^2*1-1=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}
$