28/7q+14/14-3q=9

Solution for 28/7q+14/14-3q=9 equation:

28/7q+14/14-3q=9

We move all terms to the left:

28/7q+14/14-3q-(9)=0


Domain of the equation: 7q!=0

q!=0/7

q!=0

q∈R


determiningTheFunctionDomain
28/7q-3q-9+14/14=0

We add all the numbers together, and all the variables

-3q+28/7q-8=0

We multiply all the terms by the denominator


-3q*7q-8*7q+28=0

Wy multiply elements

-21q^2-56q+28=0

a = -21; b = -56; c = +28;
Δ = b2-4ac
Δ = -562-4·(-21)·28
Δ = 5488
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5488}=\sqrt{784*7}=\sqrt{784}*\sqrt{7}=28\sqrt{7}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-28\sqrt{7}}{2*-21}=\frac{56-28\sqrt{7}}{-42}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+28\sqrt{7}}{2*-21}=\frac{56+28\sqrt{7}}{-42}
$