12-5q=2q2

Solution for 12-5q=2q2 equation:

12-5q=2q^2

We move all terms to the left:

12-5q-(2q^2)=0

determiningTheFunctionDomain
-2q^2-5q+12=0

a = -2; b = -5; c = +12;
Δ = b2-4ac
Δ = -52-4·(-2)·12
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-11}{2*-2}=\frac{-6}{-4}
=1+1/2
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+11}{2*-2}=\frac{16}{-4}
=-4
$