(x^2)-18x+61=0

Solution for (x^2)-18x+61=0 equation:

(x^2)-18x+61=0

a = 1; b = -18; c = +61;
Δ = b2-4ac
Δ = -182-4·1·61
Δ = 80
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-4\sqrt{5}}{2*1}=\frac{18-4\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+4\sqrt{5}}{2*1}=\frac{18+4\sqrt{5}}{2}
$