2/3x-9/1x=20

Solution for 2/3x-9/1x=20 equation:

2/3x-9/1x=20

We move all terms to the left:

2/3x-9/1x-(20)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 1x!=0

x∈R


We calculate fractions


2x/3x^2+(-27x)/3x^2-20=0

We multiply all the terms by the denominator


2x+(-27x)-20*3x^2=0

Wy multiply elements

-60x^2+2x+(-27x)=0

We get rid of parentheses

-60x^2+2x-27x=0

We add all the numbers together, and all the variables

-60x^2-25x=0

a = -60; b = -25; c = 0;
Δ = b2-4ac
Δ = -252-4·(-60)·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-25}{2*-60}=\frac{0}{-120}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+25}{2*-60}=\frac{50}{-120}
=-5/12
$