25*x^2+6025*x-500=0

Solution for 25*x^2+6025*x-500=0 equation:

25x^2+6025x-500=0

a = 25; b = 6025; c = -500;
Δ = b2-4ac
Δ = 60252-4·25·(-500)
Δ = 36350625
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:

$\sqrt{\Delta}=\sqrt{36350625}=\sqrt{625*58161}=\sqrt{625}*\sqrt{58161}=25\sqrt{58161}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6025)-25\sqrt{58161}}{2*25}=\frac{-6025-25\sqrt{58161}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6025)+25\sqrt{58161}}{2*25}=\frac{-6025+25\sqrt{58161}}{50}
$