31/2x-51/3x,x=2/5

Solution for 31/2x-51/3x,x=2/5 equation:

31/2x-51/3x.x=2/5

We move all terms to the left:

31/2x-51/3x.x-(2/5)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x.x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

31/2x-51/3x.x-(+2/5)=0

We get rid of parentheses

31/2x-51/3x.x-2/5=0

We calculate fractions


(-36x^2)/30x^2+465x/30x^2+(-2550x)/30x^2=0

We multiply all the terms by the denominator


(-36x^2)+465x+(-2550x)=0

We get rid of parentheses

-36x^2+465x-2550x=0

We add all the numbers together, and all the variables

-36x^2-2085x=0

a = -36; b = -2085; c = 0;
Δ = b2-4ac
Δ = -20852-4·(-36)·0
Δ = 4347225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4347225}=2085$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2085)-2085}{2*-36}=\frac{0}{-72}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2085)+2085}{2*-36}=\frac{4170}{-72}
=-57+11/12
$