6q^2+8q-1=0

Solution for 6q^2+8q-1=0 equation:

6q^2+8q-1=0

a = 6; b = 8; c = -1;
Δ = b2-4ac
Δ = 82-4·6·(-1)
Δ = 88
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:

$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{22}}{2*6}=\frac{-8-2\sqrt{22}}{12}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{22}}{2*6}=\frac{-8+2\sqrt{22}}{12}
$