(5z-1)(2+z)=0

Solution for (5z-1)(2+z)=0 equation:

(5z-1)(2+z)=0

We add all the numbers together, and all the variables

(5z-1)(z+2)=0

We multiply parentheses ..

(+5z^2+10z-1z-2)=0

We get rid of parentheses

5z^2+10z-1z-2=0

We add all the numbers together, and all the variables

5z^2+9z-2=0

a = 5; b = 9; c = -2;
Δ = b2-4ac
Δ = 92-4·5·(-2)
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{-(9)-11}{2*5}=\frac{-20}{10}
=-2
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+11}{2*5}=\frac{2}{10}
=1/5
$