0=-8z^2+11z-3

Solution for 0=-8z^2+11z-3 equation:

0=-8z^2+11z-3

We move all terms to the left:

0-(-8z^2+11z-3)=0

We add all the numbers together, and all the variables

-(-8z^2+11z-3)=0

We get rid of parentheses

8z^2-11z+3=0

a = 8; b = -11; c = +3;
Δ = b2-4ac
Δ = -112-4·8·3
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-5}{2*8}=\frac{6}{16}
=3/8
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+5}{2*8}=\frac{16}{16}
=1
$