12n^2-16n=3

Solution for 12n^2-16n=3 equation:

12n^2-16n=3

We move all terms to the left:

12n^2-16n-(3)=0

a = 12; b = -16; c = -3;
Δ = b2-4ac
Δ = -162-4·12·(-3)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-20}{2*12}=\frac{-4}{24}
=-1/6
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+20}{2*12}=\frac{36}{24}
=1+1/2
$