(5z-6)(2-z)=0

Solution for (5z-6)(2-z)=0 equation:

(5z-6)(2-z)=0

We add all the numbers together, and all the variables

(5z-6)(-1z+2)=0

We multiply parentheses ..

(-5z^2+10z+6z-12)=0

We get rid of parentheses

-5z^2+10z+6z-12=0

We add all the numbers together, and all the variables

-5z^2+16z-12=0

a = -5; b = 16; c = -12;
Δ = b2-4ac
Δ = 162-4·(-5)·(-12)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4}{2*-5}=\frac{-20}{-10}
=+2
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4}{2*-5}=\frac{-12}{-10}
=1+1/5
$