3-12n=7n^2

Solution for 3-12n=7n^2 equation:

3-12n=7n^2

We move all terms to the left:

3-12n-(7n^2)=0

determiningTheFunctionDomain
-7n^2-12n+3=0

a = -7; b = -12; c = +3;
Δ = b2-4ac
Δ = -122-4·(-7)·3
Δ = 228
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:

$\sqrt{\Delta}=\sqrt{228}=\sqrt{4*57}=\sqrt{4}*\sqrt{57}=2\sqrt{57}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{57}}{2*-7}=\frac{12-2\sqrt{57}}{-14}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{57}}{2*-7}=\frac{12+2\sqrt{57}}{-14}
$