42q^2=16q

Solution for 42q^2=16q equation:

42q^2=16q

We move all terms to the left:

42q^2-(16q)=0

a = 42; b = -16; c = 0;
Δ = b2-4ac
Δ = -162-4·42·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-16}{2*42}=\frac{0}{84}
=0
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16}{2*42}=\frac{32}{84}
=8/21
$