50n^2=-100n+50

Solution for 50n^2=-100n+50 equation:

50n^2=-100n+50

We move all terms to the left:

50n^2-(-100n+50)=0

We get rid of parentheses

50n^2+100n-50=0

a = 50; b = 100; c = -50;
Δ = b2-4ac
Δ = 1002-4·50·(-50)
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*50}=\frac{-100-100\sqrt{2}}{100}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+100\sqrt{2}}{2*50}=\frac{-100+100\sqrt{2}}{100}
$