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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-5z^2+11z-2=0

a = -5; b = 11; c = -2;
Δ = b2-4ac
Δ = 112-4·(-5)·(-2)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-9}{2*-5}=\frac{-20}{-10}
=+2
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+9}{2*-5}=\frac{-2}{-10}
=1/5
$