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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(-5z^2+25z+6z-30)=0

We get rid of parentheses

-5z^2+25z+6z-30=0

We add all the numbers together, and all the variables

-5z^2+31z-30=0

a = -5; b = 31; c = -30;
Δ = b2-4ac
Δ = 312-4·(-5)·(-30)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-19}{2*-5}=\frac{-50}{-10}
=+5
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+19}{2*-5}=\frac{-12}{-10}
=1+1/5
$