x^2-111x+1=0

Solution for x^2-111x+1=0 equation:

x^2-111x+1=0

a = 1; b = -111; c = +1;
Δ = b2-4ac
Δ = -1112-4·1·1
Δ = 12317
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-111)-\sqrt{12317}}{2*1}=\frac{111-\sqrt{12317}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-111)+\sqrt{12317}}{2*1}=\frac{111+\sqrt{12317}}{2}
$