-7z^2-2z+6=0

Solution for -7z^2-2z+6=0 equation:

-7z^2-2z+6=0

a = -7; b = -2; c = +6;
Δ = b2-4ac
Δ = -22-4·(-7)·6
Δ = 172
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{172}=\sqrt{4*43}=\sqrt{4}*\sqrt{43}=2\sqrt{43}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{43}}{2*-7}=\frac{2-2\sqrt{43}}{-14}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{43}}{2*-7}=\frac{2+2\sqrt{43}}{-14}
$