4n^2=625+100n

Solution for 4n^2=625+100n equation:

4n^2=625+100n

We move all terms to the left:

4n^2-(625+100n)=0

We add all the numbers together, and all the variables

4n^2-(100n+625)=0

We get rid of parentheses

4n^2-100n-625=0

a = 4; b = -100; c = -625;
Δ = b2-4ac
Δ = -1002-4·4·(-625)
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*4}=\frac{100-100\sqrt{2}}{8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+100\sqrt{2}}{2*4}=\frac{100+100\sqrt{2}}{8}
$