3z+8z(z-1)=25

Solution for 3z+8z(z-1)=25 equation:

3z+8z(z-1)=25

We move all terms to the left:

3z+8z(z-1)-(25)=0

We multiply parentheses

8z^2+3z-8z-25=0

We add all the numbers together, and all the variables

8z^2-5z-25=0

a = 8; b = -5; c = -25;
Δ = b2-4ac
Δ = -52-4·8·(-25)
Δ = 825
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:

$\sqrt{\Delta}=\sqrt{825}=\sqrt{25*33}=\sqrt{25}*\sqrt{33}=5\sqrt{33}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5\sqrt{33}}{2*8}=\frac{5-5\sqrt{33}}{16}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5\sqrt{33}}{2*8}=\frac{5+5\sqrt{33}}{16}
$