9n^2-6n-11=7

Solution for 9n^2-6n-11=7 equation:

9n^2-6n-11=7

We move all terms to the left:

9n^2-6n-11-(7)=0

We add all the numbers together, and all the variables

9n^2-6n-18=0

a = 9; b = -6; c = -18;
Δ = b2-4ac
Δ = -62-4·9·(-18)
Δ = 684
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:

$\sqrt{\Delta}=\sqrt{684}=\sqrt{36*19}=\sqrt{36}*\sqrt{19}=6\sqrt{19}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{19}}{2*9}=\frac{6-6\sqrt{19}}{18}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{19}}{2*9}=\frac{6+6\sqrt{19}}{18}
$