0=3z^2-4z-7

Solution for 0=3z^2-4z-7 equation:

0=3z^2-4z-7

We move all terms to the left:

0-(3z^2-4z-7)=0

We add all the numbers together, and all the variables

-(3z^2-4z-7)=0

We get rid of parentheses

-3z^2+4z+7=0

a = -3; b = 4; c = +7;
Δ = b2-4ac
Δ = 42-4·(-3)·7
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-10}{2*-3}=\frac{-14}{-6}
=2+1/3
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+10}{2*-3}=\frac{6}{-6}
=-1
$