-3(1-3n)=-12n(n-5)

Solution for -3(1-3n)=-12n(n-5) equation:

-3(1-3n)=-12n(n-5)

We move all terms to the left:

-3(1-3n)-(-12n(n-5))=0

We add all the numbers together, and all the variables

-3(-3n+1)-(-12n(n-5))=0

We multiply parentheses

9n-(-12n(n-5))-3=0


We calculate terms in parentheses: -(-12n(n-5)), so:

-12n(n-5)

We multiply parentheses

-12n^2+60n

Back to the equation:

-(-12n^2+60n)


We get rid of parentheses

12n^2-60n+9n-3=0

We add all the numbers together, and all the variables

12n^2-51n-3=0

a = 12; b = -51; c = -3;
Δ = b2-4ac
Δ = -512-4·12·(-3)
Δ = 2745
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:

$\sqrt{\Delta}=\sqrt{2745}=\sqrt{9*305}=\sqrt{9}*\sqrt{305}=3\sqrt{305}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-51)-3\sqrt{305}}{2*12}=\frac{51-3\sqrt{305}}{24}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+3\sqrt{305}}{2*12}=\frac{51+3\sqrt{305}}{24}
$