(5-z)(3z+7)=0

Solution for (5-z)(3z+7)=0 equation:

(5-z)(3z+7)=0

We add all the numbers together, and all the variables

(-1z+5)(3z+7)=0

We multiply parentheses ..

(-3z^2-7z+15z+35)=0

We get rid of parentheses

-3z^2-7z+15z+35=0

We add all the numbers together, and all the variables

-3z^2+8z+35=0

a = -3; b = 8; c = +35;
Δ = b2-4ac
Δ = 82-4·(-3)·35
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-22}{2*-3}=\frac{-30}{-6}
=+5
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+22}{2*-3}=\frac{14}{-6}
=-2+1/3
$