X^2-64x-400=0

Solution for X^2-64x-400=0 equation:

X^2-64X-400=0

a = 1; b = -64; c = -400;
Δ = b2-4ac
Δ = -642-4·1·(-400)
Δ = 5696
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:

$\sqrt{\Delta}=\sqrt{5696}=\sqrt{64*89}=\sqrt{64}*\sqrt{89}=8\sqrt{89}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-8\sqrt{89}}{2*1}=\frac{64-8\sqrt{89}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+8\sqrt{89}}{2*1}=\frac{64+8\sqrt{89}}{2}
$