-z^2+14z+4.2=0

Solution for -z^2+14z+4.2=0 equation:

-z^2+14z+4.2=0

We add all the numbers together, and all the variables

-1z^2+14z+4.2=0

a = -1; b = 14; c = +4.2;
Δ = b2-4ac
Δ = 142-4·(-1)·4.2
Δ = 212.8
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{-(14)-\sqrt{212.8}}{2*-1}=\frac{-14-\sqrt{212.8}}{-2}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+\sqrt{212.8}}{2*-1}=\frac{-14+\sqrt{212.8}}{-2}
$