(5z-4)(2+z)=0

Solution for (5z-4)(2+z)=0 equation:

(5z-4)(2+z)=0

We add all the numbers together, and all the variables

(5z-4)(z+2)=0

We multiply parentheses ..

(+5z^2+10z-4z-8)=0

We get rid of parentheses

5z^2+10z-4z-8=0

We add all the numbers together, and all the variables

5z^2+6z-8=0

a = 5; b = 6; c = -8;
Δ = b2-4ac
Δ = 62-4·5·(-8)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-14}{2*5}=\frac{-20}{10}
=-2
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+14}{2*5}=\frac{8}{10}
=4/5
$