12/1q=1/3q+2

Solution for 12/1q=1/3q+2 equation:

12/1q=1/3q+2

We move all terms to the left:

12/1q-(1/3q+2)=0


Domain of the equation: 1q!=0

q∈R



Domain of the equation: 3q+2)!=0

q∈R


We get rid of parentheses

12/1q-1/3q-2=0

We calculate fractions


36q/3q^2+(-q)/3q^2-2=0

We add all the numbers together, and all the variables

36q/3q^2+(-1q)/3q^2-2=0

We multiply all the terms by the denominator


36q+(-1q)-2*3q^2=0

Wy multiply elements

-6q^2+36q+(-1q)=0

We get rid of parentheses

-6q^2+36q-1q=0

We add all the numbers together, and all the variables

-6q^2+35q=0

a = -6; b = 35; c = 0;
Δ = b2-4ac
Δ = 352-4·(-6)·0
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-35}{2*-6}=\frac{-70}{-12}
=5+5/6
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+35}{2*-6}=\frac{0}{-12}
=0
$