(6q-1)(8q+3)=0

Solution for (6q-1)(8q+3)=0 equation:

(6q-1)(8q+3)=0

We multiply parentheses ..

(+48q^2+18q-8q-3)=0

We get rid of parentheses

48q^2+18q-8q-3=0

We add all the numbers together, and all the variables

48q^2+10q-3=0

a = 48; b = 10; c = -3;
Δ = b2-4ac
Δ = 102-4·48·(-3)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-26}{2*48}=\frac{-36}{96}
=-3/8
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+26}{2*48}=\frac{16}{96}
=1/6
$