250x^2-6175x+400=0

Solution for 250x^2-6175x+400=0 equation:

250x^2-6175x+400=0

a = 250; b = -6175; c = +400;
Δ = b2-4ac
Δ = -61752-4·250·400
Δ = 37730625
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:

$\sqrt{\Delta}=\sqrt{37730625}=\sqrt{625*60369}=\sqrt{625}*\sqrt{60369}=25\sqrt{60369}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6175)-25\sqrt{60369}}{2*250}=\frac{6175-25\sqrt{60369}}{500}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6175)+25\sqrt{60369}}{2*250}=\frac{6175+25\sqrt{60369}}{500}
$