x^2-23x-99=0

Solution for x^2-23x-99=0 equation:

x^2-23x-99=0

a = 1; b = -23; c = -99;
Δ = b2-4ac
Δ = -232-4·1·(-99)
Δ = 925
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:

$\sqrt{\Delta}=\sqrt{925}=\sqrt{25*37}=\sqrt{25}*\sqrt{37}=5\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-5\sqrt{37}}{2*1}=\frac{23-5\sqrt{37}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+5\sqrt{37}}{2*1}=\frac{23+5\sqrt{37}}{2}
$