3z^2-84z-1=0

Solution for 3z^2-84z-1=0 equation:

3z^2-84z-1=0

a = 3; b = -84; c = -1;
Δ = b2-4ac
Δ = -842-4·3·(-1)
Δ = 7068
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:

$\sqrt{\Delta}=\sqrt{7068}=\sqrt{4*1767}=\sqrt{4}*\sqrt{1767}=2\sqrt{1767}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-2\sqrt{1767}}{2*3}=\frac{84-2\sqrt{1767}}{6}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+2\sqrt{1767}}{2*3}=\frac{84+2\sqrt{1767}}{6}
$