1/2x+9=-2/3x

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

1/2x+9=-2/3x

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

1/2x+2/3x+9=0

We calculate fractions


3x/6x^2+4x/6x^2+9=0

We multiply all the terms by the denominator


3x+4x+9*6x^2=0

We add all the numbers together, and all the variables

7x+9*6x^2=0

Wy multiply elements

54x^2+7x=0

a = 54; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·54·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*54}=\frac{-14}{108}
=-7/54
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*54}=\frac{0}{108}
=0
$