2/3x+9=27-14/6x

Solution for 2/3x+9=27-14/6x equation:

2/3x+9=27-14/6x

We move all terms to the left:

2/3x+9-(27-14/6x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2/3x-(-14/6x+27)+9=0

We get rid of parentheses

2/3x+14/6x-27+9=0

We calculate fractions


12x/18x^2+42x/18x^2-27+9=0

We add all the numbers together, and all the variables

12x/18x^2+42x/18x^2-18=0

We multiply all the terms by the denominator


12x+42x-18*18x^2=0

We add all the numbers together, and all the variables

54x-18*18x^2=0

Wy multiply elements

-324x^2+54x=0

a = -324; b = 54; c = 0;
Δ = b2-4ac
Δ = 542-4·(-324)·0
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-54}{2*-324}=\frac{-108}{-648}
=1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+54}{2*-324}=\frac{0}{-648}
=0
$