z2+27=97

Solution for z2+27=97 equation:

z2+27=97

We move all terms to the left:

z2+27-(97)=0

We add all the numbers together, and all the variables

z^2-70=0

a = 1; b = 0; c = -70;
Δ = b2-4ac
Δ = 02-4·1·(-70)
Δ = 280
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:

$\sqrt{\Delta}=\sqrt{280}=\sqrt{4*70}=\sqrt{4}*\sqrt{70}=2\sqrt{70}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{70}}{2*1}=\frac{0-2\sqrt{70}}{2}
=-\frac{2\sqrt{70}}{2}
=-\sqrt{70}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{70}}{2*1}=\frac{0+2\sqrt{70}}{2}
=\frac{2\sqrt{70}}{2}
=\sqrt{70}
$