x^2+4x-384=0

Solution for x^2+4x-384=0 equation:

x^2+4x-384=0

a = 1; b = 4; c = -384;
Δ = b2-4ac
Δ = 42-4·1·(-384)
Δ = 1552
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:

$\sqrt{\Delta}=\sqrt{1552}=\sqrt{16*97}=\sqrt{16}*\sqrt{97}=4\sqrt{97}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{97}}{2*1}=\frac{-4-4\sqrt{97}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{97}}{2*1}=\frac{-4+4\sqrt{97}}{2}
$