-42z*z-14z=0

Solution for -42z*z-14z=0 equation:

-42z*z-14z=0

We add all the numbers together, and all the variables

-14z-42z*z=0

Wy multiply elements

-42z^2-14z=0

a = -42; b = -14; c = 0;
Δ = b2-4ac
Δ = -142-4·(-42)·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-14}{2*-42}=\frac{0}{-84}
=0
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14}{2*-42}=\frac{28}{-84}
=-1/3
$