12/q=2q+2

Solution for 12/q=2q+2 equation:

12/q=2q+2

We move all terms to the left:

12/q-(2q+2)=0


Domain of the equation: q!=0

q∈R


We get rid of parentheses

12/q-2q-2=0

We multiply all the terms by the denominator


-2q*q-2*q+12=0

We add all the numbers together, and all the variables

-2q-2q*q+12=0

Wy multiply elements

-2q^2-2q+12=0

a = -2; b = -2; c = +12;
Δ = b2-4ac
Δ = -22-4·(-2)·12
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-10}{2*-2}=\frac{-8}{-4}
=+2
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+10}{2*-2}=\frac{12}{-4}
=-3
$