48=z(8+z)

Solution for 48=z(8+z) equation:

48=z(8+z)

We move all terms to the left:

48-(z(8+z))=0

We add all the numbers together, and all the variables

-(z(z+8))+48=0


We calculate terms in parentheses: -(z(z+8)), so:

z(z+8)

We multiply parentheses

z^2+8z

Back to the equation:

-(z^2+8z)


We get rid of parentheses

-z^2-8z+48=0

We add all the numbers together, and all the variables

-1z^2-8z+48=0

a = -1; b = -8; c = +48;
Δ = b2-4ac
Δ = -82-4·(-1)·48
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-16}{2*-1}=\frac{-8}{-2}
=+4
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+16}{2*-1}=\frac{24}{-2}
=-12
$