3(z-2)(-z+7)=0

Solution for 3(z-2)(-z+7)=0 equation:

3(z-2)(-z+7)=0

We add all the numbers together, and all the variables

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

We multiply parentheses ..

3(-1z^2+7z+2z-14)=0

We multiply parentheses

-3z^2+21z+6z-42=0

We add all the numbers together, and all the variables

-3z^2+27z-42=0

a = -3; b = 27; c = -42;
Δ = b2-4ac
Δ = 272-4·(-3)·(-42)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-15}{2*-3}=\frac{-42}{-6}
=+7
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+15}{2*-3}=\frac{-12}{-6}
=+2
$