(4z+3)(z-2)=0

Solution for (4z+3)(z-2)=0 equation:

(4z+3)(z-2)=0

We multiply parentheses ..

(+4z^2-8z+3z-6)=0

We get rid of parentheses

4z^2-8z+3z-6=0

We add all the numbers together, and all the variables

4z^2-5z-6=0

a = 4; b = -5; c = -6;
Δ = b2-4ac
Δ = -52-4·4·(-6)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-11}{2*4}=\frac{-6}{8}
=-3/4
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+11}{2*4}=\frac{16}{8}
=2
$