-1/2x+11/6x=20/9

Solution for -1/2x+11/6x=20/9 equation:

-1/2x+11/6x=20/9

We move all terms to the left:

-1/2x+11/6x-(20/9)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

-1/2x+11/6x-(+20/9)=0

We get rid of parentheses

-1/2x+11/6x-20/9=0

We calculate fractions


(-1440x^2)/972x^2+(-486x)/972x^2+1782x/972x^2=0

We multiply all the terms by the denominator


(-1440x^2)+(-486x)+1782x=0

We add all the numbers together, and all the variables

(-1440x^2)+1782x+(-486x)=0

We get rid of parentheses

-1440x^2+1782x-486x=0

We add all the numbers together, and all the variables

-1440x^2+1296x=0

a = -1440; b = 1296; c = 0;
Δ = b2-4ac
Δ = 12962-4·(-1440)·0
Δ = 1679616
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1679616}=1296$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1296)-1296}{2*-1440}=\frac{-2592}{-2880}
=9/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1296)+1296}{2*-1440}=\frac{0}{-2880}
=0
$