-2012q(2q-44)=24

Solution for -2012q(2q-44)=24 equation:

-2012q(2q-44)=24

We move all terms to the left:

-2012q(2q-44)-(24)=0

We multiply parentheses

-4024q^2+88528q-24=0

a = -4024; b = 88528; c = -24;
Δ = b2-4ac
Δ = 885282-4·(-4024)·(-24)
Δ = 7836820480
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:

$\sqrt{\Delta}=\sqrt{7836820480}=\sqrt{1024*7653145}=\sqrt{1024}*\sqrt{7653145}=32\sqrt{7653145}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(88528)-32\sqrt{7653145}}{2*-4024}=\frac{-88528-32\sqrt{7653145}}{-8048}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(88528)+32\sqrt{7653145}}{2*-4024}=\frac{-88528+32\sqrt{7653145}}{-8048}
$