3(2n2+1)=11n

Solution for 3(2n2+1)=11n equation:

3(2n^2+1)=11n

We move all terms to the left:

3(2n^2+1)-(11n)=0

We add all the numbers together, and all the variables

-11n+3(2n^2+1)=0

We multiply parentheses

6n^2-11n+3=0

a = 6; b = -11; c = +3;
Δ = b2-4ac
Δ = -112-4·6·3
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-7}{2*6}=\frac{4}{12}
=1/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+7}{2*6}=\frac{18}{12}
=1+1/2
$