5n^2=28+13n

Solution for 5n^2=28+13n equation:

5n^2=28+13n

We move all terms to the left:

5n^2-(28+13n)=0

We add all the numbers together, and all the variables

5n^2-(13n+28)=0

We get rid of parentheses

5n^2-13n-28=0

a = 5; b = -13; c = -28;
Δ = b2-4ac
Δ = -132-4·5·(-28)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-27}{2*5}=\frac{-14}{10}
=-1+2/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+27}{2*5}=\frac{40}{10}
=4
$