5n^2-25n+n^2=25

Solution for 5n^2-25n+n^2=25 equation:

5n^2-25n+n^2=25

We move all terms to the left:

5n^2-25n+n^2-(25)=0

We add all the numbers together, and all the variables

6n^2-25n-25=0

a = 6; b = -25; c = -25;
Δ = b2-4ac
Δ = -252-4·6·(-25)
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-35}{2*6}=\frac{-10}{12}
=-5/6
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+35}{2*6}=\frac{60}{12}
=5
$