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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(-5z^2+35z+3z-21)=0

We get rid of parentheses

-5z^2+35z+3z-21=0

We add all the numbers together, and all the variables

-5z^2+38z-21=0

a = -5; b = 38; c = -21;
Δ = b2-4ac
Δ = 382-4·(-5)·(-21)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-32}{2*-5}=\frac{-70}{-10}
=+7
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+32}{2*-5}=\frac{-6}{-10}
=3/5
$