14n^2-1=4+4n^2-12n

Solution for 14n^2-1=4+4n^2-12n equation:

14n^2-1=4+4n^2-12n

We move all terms to the left:

14n^2-1-(4+4n^2-12n)=0

We get rid of parentheses

14n^2-4n^2+12n-4-1=0

We add all the numbers together, and all the variables

10n^2+12n-5=0

a = 10; b = 12; c = -5;
Δ = b2-4ac
Δ = 122-4·10·(-5)
Δ = 344
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:

$\sqrt{\Delta}=\sqrt{344}=\sqrt{4*86}=\sqrt{4}*\sqrt{86}=2\sqrt{86}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{86}}{2*10}=\frac{-12-2\sqrt{86}}{20}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{86}}{2*10}=\frac{-12+2\sqrt{86}}{20}
$