-z^2+1z+14=0

Solution for -z^2+1z+14=0 equation:

-z^2+1z+14=0

We add all the numbers together, and all the variables

-1z^2+z+14=0

a = -1; b = 1; c = +14;
Δ = b2-4ac
Δ = 12-4·(-1)·14
Δ = 57
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{-(1)-\sqrt{57}}{2*-1}=\frac{-1-\sqrt{57}}{-2}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{57}}{2*-1}=\frac{-1+\sqrt{57}}{-2}
$