X^2+200x-2400=0

Solution for X^2+200x-2400=0 equation:

X^2+200X-2400=0

a = 1; b = 200; c = -2400;
Δ = b2-4ac
Δ = 2002-4·1·(-2400)
Δ = 49600
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:

$\sqrt{\Delta}=\sqrt{49600}=\sqrt{1600*31}=\sqrt{1600}*\sqrt{31}=40\sqrt{31}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(200)-40\sqrt{31}}{2*1}=\frac{-200-40\sqrt{31}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(200)+40\sqrt{31}}{2*1}=\frac{-200+40\sqrt{31}}{2}
$