x^2-38x-91=0

Solution for x^2-38x-91=0 equation:

x^2-38x-91=0

a = 1; b = -38; c = -91;
Δ = b2-4ac
Δ = -382-4·1·(-91)
Δ = 1808
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:

$\sqrt{\Delta}=\sqrt{1808}=\sqrt{16*113}=\sqrt{16}*\sqrt{113}=4\sqrt{113}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-4\sqrt{113}}{2*1}=\frac{38-4\sqrt{113}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+4\sqrt{113}}{2*1}=\frac{38+4\sqrt{113}}{2}
$