z2-8z=49

Solution for z2-8z=49 equation:

z2-8z=49

We move all terms to the left:

z2-8z-(49)=0

We add all the numbers together, and all the variables

z^2-8z-49=0

a = 1; b = -8; c = -49;
Δ = b2-4ac
Δ = -82-4·1·(-49)
Δ = 260
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:

$\sqrt{\Delta}=\sqrt{260}=\sqrt{4*65}=\sqrt{4}*\sqrt{65}=2\sqrt{65}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{65}}{2*1}=\frac{8-2\sqrt{65}}{2}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{65}}{2*1}=\frac{8+2\sqrt{65}}{2}
$