3z(2z+9)-15=0

Solution for 3z(2z+9)-15=0 equation:

3z(2z+9)-15=0

We multiply parentheses

6z^2+27z-15=0

a = 6; b = 27; c = -15;
Δ = b2-4ac
Δ = 272-4·6·(-15)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-33}{2*6}=\frac{-60}{12}
=-5
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+33}{2*6}=\frac{6}{12}
=1/2
$