250x^2+500x-210=0

Solution for 250x^2+500x-210=0 equation:

250x^2+500x-210=0

a = 250; b = 500; c = -210;
Δ = b2-4ac
Δ = 5002-4·250·(-210)
Δ = 460000
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:

$\sqrt{\Delta}=\sqrt{460000}=\sqrt{10000*46}=\sqrt{10000}*\sqrt{46}=100\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(500)-100\sqrt{46}}{2*250}=\frac{-500-100\sqrt{46}}{500}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(500)+100\sqrt{46}}{2*250}=\frac{-500+100\sqrt{46}}{500}
$