X^2+12x-6400=0

Solution for X^2+12x-6400=0 equation:

X^2+12X-6400=0

a = 1; b = 12; c = -6400;
Δ = b2-4ac
Δ = 122-4·1·(-6400)
Δ = 25744
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:

$\sqrt{\Delta}=\sqrt{25744}=\sqrt{16*1609}=\sqrt{16}*\sqrt{1609}=4\sqrt{1609}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{1609}}{2*1}=\frac{-12-4\sqrt{1609}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{1609}}{2*1}=\frac{-12+4\sqrt{1609}}{2}
$