(2z-9)(7-z)=0

Solution for (2z-9)(7-z)=0 equation:

(2z-9)(7-z)=0

We add all the numbers together, and all the variables

(2z-9)(-1z+7)=0

We multiply parentheses ..

(-2z^2+14z+9z-63)=0

We get rid of parentheses

-2z^2+14z+9z-63=0

We add all the numbers together, and all the variables

-2z^2+23z-63=0

a = -2; b = 23; c = -63;
Δ = b2-4ac
Δ = 232-4·(-2)·(-63)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-5}{2*-2}=\frac{-28}{-4}
=+7
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+5}{2*-2}=\frac{-18}{-4}
=4+1/2
$