975=n*(195-5n)

Solution for 975=n*(195-5n) equation:

975=n(195-5n)

We move all terms to the left:

975-(n(195-5n))=0

We add all the numbers together, and all the variables

-(n(-5n+195))+975=0


We calculate terms in parentheses: -(n(-5n+195)), so:

n(-5n+195)

We multiply parentheses

-5n^2+195n

Back to the equation:

-(-5n^2+195n)


We get rid of parentheses

5n^2-195n+975=0

a = 5; b = -195; c = +975;
Δ = b2-4ac
Δ = -1952-4·5·975
Δ = 18525
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:

$\sqrt{\Delta}=\sqrt{18525}=\sqrt{25*741}=\sqrt{25}*\sqrt{741}=5\sqrt{741}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-195)-5\sqrt{741}}{2*5}=\frac{195-5\sqrt{741}}{10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-195)+5\sqrt{741}}{2*5}=\frac{195+5\sqrt{741}}{10}
$