3/q+3q=6q

Solution for 3/q+3q=6q equation:

3/q+3q=6q

We move all terms to the left:

3/q+3q-(6q)=0


Domain of the equation: q!=0

q∈R


We add all the numbers together, and all the variables

-3q+3/q=0

We multiply all the terms by the denominator


-3q*q+3=0

Wy multiply elements

-3q^2+3=0

a = -3; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-3)·3
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6}{2*-3}=\frac{-6}{-6}
=1
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6}{2*-3}=\frac{6}{-6}
=-1
$