5x^2-125x-500=0

Solution for 5x^2-125x-500=0 equation:

5x^2-125x-500=0

a = 5; b = -125; c = -500;
Δ = b2-4ac
Δ = -1252-4·5·(-500)
Δ = 25625
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:

$\sqrt{\Delta}=\sqrt{25625}=\sqrt{625*41}=\sqrt{625}*\sqrt{41}=25\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-125)-25\sqrt{41}}{2*5}=\frac{125-25\sqrt{41}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-125)+25\sqrt{41}}{2*5}=\frac{125+25\sqrt{41}}{10}
$