10n^2+100n=250

Solution for 10n^2+100n=250 equation:

10n^2+100n=250

We move all terms to the left:

10n^2+100n-(250)=0

a = 10; b = 100; c = -250;
Δ = b2-4ac
Δ = 1002-4·10·(-250)
Δ = 20000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{20000}=\sqrt{10000*2}=\sqrt{10000}*\sqrt{2}=100\sqrt{2}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-100\sqrt{2}}{2*10}=\frac{-100-100\sqrt{2}}{20}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+100\sqrt{2}}{2*10}=\frac{-100+100\sqrt{2}}{20}
$