6n^2=52-11n

Solution for 6n^2=52-11n equation:

6n^2=52-11n

We move all terms to the left:

6n^2-(52-11n)=0

We add all the numbers together, and all the variables

6n^2-(-11n+52)=0

We get rid of parentheses

6n^2+11n-52=0

a = 6; b = 11; c = -52;
Δ = b2-4ac
Δ = 112-4·6·(-52)
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-37}{2*6}=\frac{-48}{12}
=-4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+37}{2*6}=\frac{26}{12}
=2+1/6
$