6.4+2.1z(z-2)=8.5

Solution for 6.4+2.1z(z-2)=8.5 equation:

6.4+2.1z(z-2)=8.5

We move all terms to the left:

6.4+2.1z(z-2)-(8.5)=0

We add all the numbers together, and all the variables

2.1z(z-2)-2.1=0

We multiply parentheses

2z^2-4z-2.1=0

a = 2; b = -4; c = -2.1;
Δ = b2-4ac
Δ = -42-4·2·(-2.1)
Δ = 32.8
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-\sqrt{32.8}}{2*2}=\frac{4-\sqrt{32.8}}{4}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+\sqrt{32.8}}{2*2}=\frac{4+\sqrt{32.8}}{4}
$