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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

5(-1z^2+7z-9z+63)=0

We multiply parentheses

-5z^2+35z-45z+315=0

We add all the numbers together, and all the variables

-5z^2-10z+315=0

a = -5; b = -10; c = +315;
Δ = b2-4ac
Δ = -102-4·(-5)·315
Δ = 6400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6400}=80$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-80}{2*-5}=\frac{-70}{-10}
=+7
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+80}{2*-5}=\frac{90}{-10}
=-9
$