x^2+4x-16384=0

Solution for x^2+4x-16384=0 equation:

x^2+4x-16384=0

a = 1; b = 4; c = -16384;
Δ = b2-4ac
Δ = 42-4·1·(-16384)
Δ = 65552
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:

$\sqrt{\Delta}=\sqrt{65552}=\sqrt{16*4097}=\sqrt{16}*\sqrt{4097}=4\sqrt{4097}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{4097}}{2*1}=\frac{-4-4\sqrt{4097}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{4097}}{2*1}=\frac{-4+4\sqrt{4097}}{2}
$