z^2-18z+26=0

Solution for z^2-18z+26=0 equation:

z^2-18z+26=0

a = 1; b = -18; c = +26;
Δ = b2-4ac
Δ = -182-4·1·26
Δ = 220
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:

$\sqrt{\Delta}=\sqrt{220}=\sqrt{4*55}=\sqrt{4}*\sqrt{55}=2\sqrt{55}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{55}}{2*1}=\frac{18-2\sqrt{55}}{2}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{55}}{2*1}=\frac{18+2\sqrt{55}}{2}
$