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 = 568
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:

$\sqrt{\Delta}=\sqrt{568}=\sqrt{4*142}=\sqrt{4}*\sqrt{142}=2\sqrt{142}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{142}}{2*1}=\frac{18-2\sqrt{142}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{142}}{2*1}=\frac{18+2\sqrt{142}}{2}
$