(9z-3)(5z+6)=0

Solution for (9z-3)(5z+6)=0 equation:

(9z-3)(5z+6)=0

We multiply parentheses ..

(+45z^2+54z-15z-18)=0

We get rid of parentheses

45z^2+54z-15z-18=0

We add all the numbers together, and all the variables

45z^2+39z-18=0

a = 45; b = 39; c = -18;
Δ = b2-4ac
Δ = 392-4·45·(-18)
Δ = 4761
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4761}=69$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(39)-69}{2*45}=\frac{-108}{90}
=-1+1/5
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+69}{2*45}=\frac{30}{90}
=1/3
$