0=15z^2+z-2

Solution for 0=15z^2+z-2 equation:

0=15z^2+z-2

We move all terms to the left:

0-(15z^2+z-2)=0

We add all the numbers together, and all the variables

-(15z^2+z-2)=0

We get rid of parentheses

-15z^2-z+2=0

We add all the numbers together, and all the variables

-15z^2-1z+2=0

a = -15; b = -1; c = +2;
Δ = b2-4ac
Δ = -12-4·(-15)·2
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-11}{2*-15}=\frac{-10}{-30}
=1/3
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+11}{2*-15}=\frac{12}{-30}
=-2/5
$