x^2-40x-6587=0

Solution for x^2-40x-6587=0 equation:

x^2-40x-6587=0

a = 1; b = -40; c = -6587;
Δ = b2-4ac
Δ = -402-4·1·(-6587)
Δ = 27948
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:

$\sqrt{\Delta}=\sqrt{27948}=\sqrt{4*6987}=\sqrt{4}*\sqrt{6987}=2\sqrt{6987}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-2\sqrt{6987}}{2*1}=\frac{40-2\sqrt{6987}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+2\sqrt{6987}}{2*1}=\frac{40+2\sqrt{6987}}{2}
$