56q^2-384=-400q

Solution for 56q^2-384=-400q equation:

56q^2-384=-400q

We move all terms to the left:

56q^2-384-(-400q)=0

We get rid of parentheses

56q^2+400q-384=0

a = 56; b = 400; c = -384;
Δ = b2-4ac
Δ = 4002-4·56·(-384)
Δ = 246016
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{246016}=496$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(400)-496}{2*56}=\frac{-896}{112}
=-8
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(400)+496}{2*56}=\frac{96}{112}
=6/7
$