(7-z)(5z-9)=0

Solution for (7-z)(5z-9)=0 equation:

(7-z)(5z-9)=0

We add all the numbers together, and all the variables

(-1z+7)(5z-9)=0

We multiply parentheses ..

(-5z^2+9z+35z-63)=0

We get rid of parentheses

-5z^2+9z+35z-63=0

We add all the numbers together, and all the variables

-5z^2+44z-63=0

a = -5; b = 44; c = -63;
Δ = b2-4ac
Δ = 442-4·(-5)·(-63)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-26}{2*-5}=\frac{-70}{-10}
=+7
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+26}{2*-5}=\frac{-18}{-10}
=1+4/5
$