44=7z+z^2

Solution for 44=7z+z^2 equation:

44=7z+z^2

We move all terms to the left:

44-(7z+z^2)=0

We get rid of parentheses

-z^2-7z+44=0

We add all the numbers together, and all the variables

-1z^2-7z+44=0

a = -1; b = -7; c = +44;
Δ = b2-4ac
Δ = -72-4·(-1)·44
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{-(-7)-15}{2*-1}=\frac{-8}{-2}
=+4
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+15}{2*-1}=\frac{22}{-2}
=-11
$