(5z-1)(z+3)=0

Solution for (5z-1)(z+3)=0 equation:

(5z-1)(z+3)=0

We multiply parentheses ..

(+5z^2+15z-1z-3)=0

We get rid of parentheses

5z^2+15z-1z-3=0

We add all the numbers together, and all the variables

5z^2+14z-3=0

a = 5; b = 14; c = -3;
Δ = b2-4ac
Δ = 142-4·5·(-3)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-16}{2*5}=\frac{-30}{10}
=-3
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+16}{2*5}=\frac{2}{10}
=1/5
$