3z^2-8z-6=0

Solution for 3z^2-8z-6=0 equation:

3z^2-8z-6=0

a = 3; b = -8; c = -6;
Δ = b2-4ac
Δ = -82-4·3·(-6)
Δ = 136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{34}}{2*3}=\frac{8-2\sqrt{34}}{6}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{34}}{2*3}=\frac{8+2\sqrt{34}}{6}
$