z(-7z=21)

Solution for z(-7z=21) equation:

z(-7z=21)

We move all terms to the left:

z(-7z-(21))=0

We multiply parentheses

-7z^2-21z=0

a = -7; b = -21; c = 0;
Δ = b2-4ac
Δ = -212-4·(-7)·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-21}{2*-7}=\frac{0}{-14}
=0
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+21}{2*-7}=\frac{42}{-14}
=-3
$