x2-8x-420=0

Solution for x2-8x-420=0 equation:

x2-8x-420=0

We add all the numbers together, and all the variables

x^2-8x-420=0

a = 1; b = -8; c = -420;
Δ = b2-4ac
Δ = -82-4·1·(-420)
Δ = 1744
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:

$\sqrt{\Delta}=\sqrt{1744}=\sqrt{16*109}=\sqrt{16}*\sqrt{109}=4\sqrt{109}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{109}}{2*1}=\frac{8-4\sqrt{109}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{109}}{2*1}=\frac{8+4\sqrt{109}}{2}
$