2/3x=15x

Solution for 2/3x=15x equation:

2/3x=15x

We move all terms to the left:

2/3x-(15x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-15x+2/3x=0

We multiply all the terms by the denominator


-15x*3x+2=0

Wy multiply elements

-45x^2+2=0

a = -45; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-45)·2
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*-45}=\frac{0-6\sqrt{10}}{-90}
=-\frac{6\sqrt{10}}{-90}
=-\frac{\sqrt{10}}{-15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{10}}{2*-45}=\frac{0+6\sqrt{10}}{-90}
=\frac{6\sqrt{10}}{-90}
=\frac{\sqrt{10}}{-15}
$