96-4q=q^2

Solution for 96-4q=q^2 equation:

96-4q=q^2

We move all terms to the left:

96-4q-(q^2)=0

determiningTheFunctionDomain
-q^2-4q+96=0

We add all the numbers together, and all the variables

-1q^2-4q+96=0

a = -1; b = -4; c = +96;
Δ = b2-4ac
Δ = -42-4·(-1)·96
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-20}{2*-1}=\frac{-16}{-2}
=+8
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+20}{2*-1}=\frac{24}{-2}
=-12
$