(z2+8z)2+23(z2+8z)+112=0

Solution for (z2+8z)2+23(z2+8z)+112=0 equation:

(z2+8z)2+23(z2+8z)+112=0

We add all the numbers together, and all the variables

(+z^2+8z)2+23(+z^2+8z)+112=0

We multiply parentheses

2z^2+23z^2+16z+184z+112=0

We add all the numbers together, and all the variables

25z^2+200z+112=0

a = 25; b = 200; c = +112;
Δ = b2-4ac
Δ = 2002-4·25·112
Δ = 28800
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{28800}=\sqrt{14400*2}=\sqrt{14400}*\sqrt{2}=120\sqrt{2}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(200)-120\sqrt{2}}{2*25}=\frac{-200-120\sqrt{2}}{50}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(200)+120\sqrt{2}}{2*25}=\frac{-200+120\sqrt{2}}{50}
$