s^2-12s-110=0

Solution for s^2-12s-110=0 equation:

s^2-12s-110=0

a = 1; b = -12; c = -110;
Δ = b2-4ac
Δ = -122-4·1·(-110)
Δ = 584
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{584}=\sqrt{4*146}=\sqrt{4}*\sqrt{146}=2\sqrt{146}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{146}}{2*1}=\frac{12-2\sqrt{146}}{2}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{146}}{2*1}=\frac{12+2\sqrt{146}}{2}
$