x^2-19x-91=0

Solution for x^2-19x-91=0 equation:

x^2-19x-91=0

a = 1; b = -19; c = -91;
Δ = b2-4ac
Δ = -192-4·1·(-91)
Δ = 725
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:

$\sqrt{\Delta}=\sqrt{725}=\sqrt{25*29}=\sqrt{25}*\sqrt{29}=5\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-5\sqrt{29}}{2*1}=\frac{19-5\sqrt{29}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+5\sqrt{29}}{2*1}=\frac{19+5\sqrt{29}}{2}
$