25-6n=2n(12n-1)

Solution for 25-6n=2n(12n-1) equation:

25-6n=2n(12n-1)

We move all terms to the left:

25-6n-(2n(12n-1))=0


We calculate terms in parentheses: -(2n(12n-1)), so:

2n(12n-1)

We multiply parentheses

24n^2-2n

Back to the equation:

-(24n^2-2n)


We get rid of parentheses

-24n^2-6n+2n+25=0

We add all the numbers together, and all the variables

-24n^2-4n+25=0

a = -24; b = -4; c = +25;
Δ = b2-4ac
Δ = -42-4·(-24)·25
Δ = 2416
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:

$\sqrt{\Delta}=\sqrt{2416}=\sqrt{16*151}=\sqrt{16}*\sqrt{151}=4\sqrt{151}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{151}}{2*-24}=\frac{4-4\sqrt{151}}{-48}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{151}}{2*-24}=\frac{4+4\sqrt{151}}{-48}
$