3(z^2-0.01)-0.1z=0.3

Solution for 3(z^2-0.01)-0.1z=0.3 equation:

3(z^2-0.01)-0.1z=0.3

We move all terms to the left:

3(z^2-0.01)-0.1z-(0.3)=0

We add all the numbers together, and all the variables

-0.1z+3(z^2-0.01)-0.3=0

We multiply parentheses

3z^2-0.1z-0.03-0.3=0

We add all the numbers together, and all the variables

3z^2-0.1z-0.33=0

a = 3; b = -0.1; c = -0.33;
Δ = b2-4ac
Δ = -0.12-4·3·(-0.33)
Δ = 3.97
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{-(-0.1)-\sqrt{3.97}}{2*3}=\frac{0.1-\sqrt{3.97}}{6}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.1)+\sqrt{3.97}}{2*3}=\frac{0.1+\sqrt{3.97}}{6}
$