x^2-152x-2400=0

Solution for x^2-152x-2400=0 equation:

x^2-152x-2400=0

a = 1; b = -152; c = -2400;
Δ = b2-4ac
Δ = -1522-4·1·(-2400)
Δ = 32704
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:

$\sqrt{\Delta}=\sqrt{32704}=\sqrt{64*511}=\sqrt{64}*\sqrt{511}=8\sqrt{511}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-152)-8\sqrt{511}}{2*1}=\frac{152-8\sqrt{511}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-152)+8\sqrt{511}}{2*1}=\frac{152+8\sqrt{511}}{2}
$