12n^2-10=12n

Solution for 12n^2-10=12n equation:

12n^2-10=12n

We move all terms to the left:

12n^2-10-(12n)=0

a = 12; b = -12; c = -10;
Δ = b2-4ac
Δ = -122-4·12·(-10)
Δ = 624
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:

$\sqrt{\Delta}=\sqrt{624}=\sqrt{16*39}=\sqrt{16}*\sqrt{39}=4\sqrt{39}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{39}}{2*12}=\frac{12-4\sqrt{39}}{24}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{39}}{2*12}=\frac{12+4\sqrt{39}}{24}
$