X2-40x-20=0

Solution for X2-40x-20=0 equation:

X2-40X-20=0

We add all the numbers together, and all the variables

X^2-40X-20=0

a = 1; b = -40; c = -20;
Δ = b2-4ac
Δ = -402-4·1·(-20)
Δ = 1680
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:

$\sqrt{\Delta}=\sqrt{1680}=\sqrt{16*105}=\sqrt{16}*\sqrt{105}=4\sqrt{105}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-4\sqrt{105}}{2*1}=\frac{40-4\sqrt{105}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+4\sqrt{105}}{2*1}=\frac{40+4\sqrt{105}}{2}
$