975=n*(195n-5n)

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

975=n(195n-5n)

We move all terms to the left:

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

We add all the numbers together, and all the variables

-(n(+190n))+975=0


We calculate terms in parentheses: -(n(+190n)), so:

n(+190n)

We multiply parentheses

190n^2

Back to the equation:

-(190n^2)


a = -190; b = 0; c = +975;
Δ = b2-4ac
Δ = 02-4·(-190)·975
Δ = 741000
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:

$\sqrt{\Delta}=\sqrt{741000}=\sqrt{100*7410}=\sqrt{100}*\sqrt{7410}=10\sqrt{7410}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{7410}}{2*-190}=\frac{0-10\sqrt{7410}}{-380}
=-\frac{10\sqrt{7410}}{-380}
=-\frac{\sqrt{7410}}{-38}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{7410}}{2*-190}=\frac{0+10\sqrt{7410}}{-380}
=\frac{10\sqrt{7410}}{-380}
=\frac{\sqrt{7410}}{-38}
$