x^2-25x-500=0

Solution for x^2-25x-500=0 equation:

x^2-25x-500=0

a = 1; b = -25; c = -500;
Δ = b2-4ac
Δ = -252-4·1·(-500)
Δ = 2625
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:

$\sqrt{\Delta}=\sqrt{2625}=\sqrt{25*105}=\sqrt{25}*\sqrt{105}=5\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-5\sqrt{105}}{2*1}=\frac{25-5\sqrt{105}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+5\sqrt{105}}{2*1}=\frac{25+5\sqrt{105}}{2}
$