X^2-380x-10500=0

Solution for X^2-380x-10500=0 equation:

X^2-380X-10500=0

a = 1; b = -380; c = -10500;
Δ = b2-4ac
Δ = -3802-4·1·(-10500)
Δ = 186400
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:

$\sqrt{\Delta}=\sqrt{186400}=\sqrt{400*466}=\sqrt{400}*\sqrt{466}=20\sqrt{466}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-380)-20\sqrt{466}}{2*1}=\frac{380-20\sqrt{466}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-380)+20\sqrt{466}}{2*1}=\frac{380+20\sqrt{466}}{2}
$