(3z-7)(9-z)=0

Solution for (3z-7)(9-z)=0 equation:

(3z-7)(9-z)=0

We add all the numbers together, and all the variables

(3z-7)(-1z+9)=0

We multiply parentheses ..

(-3z^2+27z+7z-63)=0

We get rid of parentheses

-3z^2+27z+7z-63=0

We add all the numbers together, and all the variables

-3z^2+34z-63=0

a = -3; b = 34; c = -63;
Δ = b2-4ac
Δ = 342-4·(-3)·(-63)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-20}{2*-3}=\frac{-54}{-6}
=+9
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+20}{2*-3}=\frac{-14}{-6}
=2+1/3
$