6z^2+30z-54=0

Solution for 6z^2+30z-54=0 equation:

6z^2+30z-54=0

a = 6; b = 30; c = -54;
Δ = b2-4ac
Δ = 302-4·6·(-54)
Δ = 2196
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:

$\sqrt{\Delta}=\sqrt{2196}=\sqrt{36*61}=\sqrt{36}*\sqrt{61}=6\sqrt{61}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-6\sqrt{61}}{2*6}=\frac{-30-6\sqrt{61}}{12}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+6\sqrt{61}}{2*6}=\frac{-30+6\sqrt{61}}{12}
$