z^2-78z-47=0

Solution for z^2-78z-47=0 equation:

z^2-78z-47=0

a = 1; b = -78; c = -47;
Δ = b2-4ac
Δ = -782-4·1·(-47)
Δ = 6272
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:

$\sqrt{\Delta}=\sqrt{6272}=\sqrt{3136*2}=\sqrt{3136}*\sqrt{2}=56\sqrt{2}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-78)-56\sqrt{2}}{2*1}=\frac{78-56\sqrt{2}}{2}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-78)+56\sqrt{2}}{2*1}=\frac{78+56\sqrt{2}}{2}
$