9q/q^2=2

Solution for 9q/q^2=2 equation:

9q/q^2=2

We move all terms to the left:

9q/q^2-(2)=0


Domain of the equation: q^2!=0

q^2!=0/

q^2!=√0

q!=0

q∈R


We multiply all the terms by the denominator


9q-2*q^2=0

We add all the numbers together, and all the variables

-2q^2+9q=0

a = -2; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-2)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*-2}=\frac{-18}{-4}
=4+1/2
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-2}=\frac{0}{-4}
=0
$