0=9z^2+61z-14

Solution for 0=9z^2+61z-14 equation:

0=9z^2+61z-14

We move all terms to the left:

0-(9z^2+61z-14)=0

We add all the numbers together, and all the variables

-(9z^2+61z-14)=0

We get rid of parentheses

-9z^2-61z+14=0

a = -9; b = -61; c = +14;
Δ = b2-4ac
Δ = -612-4·(-9)·14
Δ = 4225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4225}=65$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-61)-65}{2*-9}=\frac{-4}{-18}
=2/9
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-61)+65}{2*-9}=\frac{126}{-18}
=-7
$