x^2-185x-4650=0

Solution for x^2-185x-4650=0 equation:

x^2-185x-4650=0

a = 1; b = -185; c = -4650;
Δ = b2-4ac
Δ = -1852-4·1·(-4650)
Δ = 52825
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:

$\sqrt{\Delta}=\sqrt{52825}=\sqrt{25*2113}=\sqrt{25}*\sqrt{2113}=5\sqrt{2113}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-185)-5\sqrt{2113}}{2*1}=\frac{185-5\sqrt{2113}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-185)+5\sqrt{2113}}{2*1}=\frac{185+5\sqrt{2113}}{2}
$