6n^2-4n-22=-11

Solution for 6n^2-4n-22=-11 equation:

6n^2-4n-22=-11

We move all terms to the left:

6n^2-4n-22-(-11)=0

We add all the numbers together, and all the variables

6n^2-4n-11=0

a = 6; b = -4; c = -11;
Δ = b2-4ac
Δ = -42-4·6·(-11)
Δ = 280
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:

$\sqrt{\Delta}=\sqrt{280}=\sqrt{4*70}=\sqrt{4}*\sqrt{70}=2\sqrt{70}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{70}}{2*6}=\frac{4-2\sqrt{70}}{12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{70}}{2*6}=\frac{4+2\sqrt{70}}{12}
$