5/12q+1/2q=33

Solution for 5/12q+1/2q=33 equation:

5/12q+1/2q=33

We move all terms to the left:

5/12q+1/2q-(33)=0


Domain of the equation: 12q!=0

q!=0/12

q!=0

q∈R



Domain of the equation: 2q!=0

q!=0/2

q!=0

q∈R


We calculate fractions


10q/24q^2+12q/24q^2-33=0

We multiply all the terms by the denominator


10q+12q-33*24q^2=0

We add all the numbers together, and all the variables

22q-33*24q^2=0

Wy multiply elements

-792q^2+22q=0

a = -792; b = 22; c = 0;
Δ = b2-4ac
Δ = 222-4·(-792)·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-22}{2*-792}=\frac{-44}{-1584}
=1/36
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+22}{2*-792}=\frac{0}{-1584}
=0
$