5n+250=-0.05n^2+20n

Solution for 5n+250=-0.05n^2+20n equation:

5n+250=-0.05n^2+20n

We move all terms to the left:

5n+250-(-0.05n^2+20n)=0

We get rid of parentheses

0.05n^2-20n+5n+250=0

We add all the numbers together, and all the variables

0.05n^2-15n+250=0

a = 0.05; b = -15; c = +250;
Δ = b2-4ac
Δ = -152-4·0.05·250
Δ = 175
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:

$\sqrt{\Delta}=\sqrt{175}=\sqrt{25*7}=\sqrt{25}*\sqrt{7}=5\sqrt{7}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-5\sqrt{7}}{2*0.05}=\frac{15-5\sqrt{7}}{0.1}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+5\sqrt{7}}{2*0.05}=\frac{15+5\sqrt{7}}{0.1}
$