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

Solution for (5z-1)(6-z)=0 equation:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-5z^2+31z-6=0

a = -5; b = 31; c = -6;
Δ = b2-4ac
Δ = 312-4·(-5)·(-6)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-29}{2*-5}=\frac{-60}{-10}
=+6
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+29}{2*-5}=\frac{-2}{-10}
=1/5
$