(3z-7)(8-z)=0

Solution for (3z-7)(8-z)=0 equation:

(3z-7)(8-z)=0

We add all the numbers together, and all the variables

(3z-7)(-1z+8)=0

We multiply parentheses ..

(-3z^2+24z+7z-56)=0

We get rid of parentheses

-3z^2+24z+7z-56=0

We add all the numbers together, and all the variables

-3z^2+31z-56=0

a = -3; b = 31; c = -56;
Δ = b2-4ac
Δ = 312-4·(-3)·(-56)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-17}{2*-3}=\frac{-48}{-6}
=+8
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+17}{2*-3}=\frac{-14}{-6}
=2+1/3
$