x^2-9x-111=0

Solution for x^2-9x-111=0 equation:

x^2-9x-111=0

a = 1; b = -9; c = -111;
Δ = b2-4ac
Δ = -92-4·1·(-111)
Δ = 525
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:

$\sqrt{\Delta}=\sqrt{525}=\sqrt{25*21}=\sqrt{25}*\sqrt{21}=5\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-5\sqrt{21}}{2*1}=\frac{9-5\sqrt{21}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+5\sqrt{21}}{2*1}=\frac{9+5\sqrt{21}}{2}
$