-6/q+9=4/2q+6

Solution for -6/q+9=4/2q+6 equation:

-6/q+9=4/2q+6

We move all terms to the left:

-6/q+9-(4/2q+6)=0


Domain of the equation: q!=0

q∈R



Domain of the equation: 2q+6)!=0

q∈R


We get rid of parentheses

-6/q-4/2q-6+9=0

We calculate fractions


(-12q)/2q^2+(-4q)/2q^2-6+9=0

We add all the numbers together, and all the variables

(-12q)/2q^2+(-4q)/2q^2+3=0

We multiply all the terms by the denominator


(-12q)+(-4q)+3*2q^2=0

Wy multiply elements

6q^2+(-12q)+(-4q)=0

We get rid of parentheses

6q^2-12q-4q=0

We add all the numbers together, and all the variables

6q^2-16q=0

a = 6; b = -16; c = 0;
Δ = b2-4ac
Δ = -162-4·6·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-16}{2*6}=\frac{0}{12}
=0
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16}{2*6}=\frac{32}{12}
=2+2/3
$