2/3x=5x

Solution for 2/3x=5x equation:

2/3x=5x

We move all terms to the left:

2/3x-(5x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-5x+2/3x=0

We multiply all the terms by the denominator


-5x*3x+2=0

Wy multiply elements

-15x^2+2=0

a = -15; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-15)·2
Δ = 120
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:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{30}}{2*-15}=\frac{0-2\sqrt{30}}{-30}
=-\frac{2\sqrt{30}}{-30}
=-\frac{\sqrt{30}}{-15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{30}}{2*-15}=\frac{0+2\sqrt{30}}{-30}
=\frac{2\sqrt{30}}{-30}
=\frac{\sqrt{30}}{-15}
$