21-4z-z^2=0

Solution for 21-4z-z^2=0 equation:

21-4z-z^2=0

We add all the numbers together, and all the variables

-1z^2-4z+21=0

a = -1; b = -4; c = +21;
Δ = b2-4ac
Δ = -42-4·(-1)·21
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-10}{2*-1}=\frac{-6}{-2}
=+3
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+10}{2*-1}=\frac{14}{-2}
=-7
$