(5z-6)(8-z)=0

Solution for (5z-6)(8-z)=0 equation:

(5z-6)(8-z)=0

We add all the numbers together, and all the variables

(5z-6)(-1z+8)=0

We multiply parentheses ..

(-5z^2+40z+6z-48)=0

We get rid of parentheses

-5z^2+40z+6z-48=0

We add all the numbers together, and all the variables

-5z^2+46z-48=0

a = -5; b = 46; c = -48;
Δ = b2-4ac
Δ = 462-4·(-5)·(-48)
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46)-34}{2*-5}=\frac{-80}{-10}
=+8
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+34}{2*-5}=\frac{-12}{-10}
=1+1/5
$