7n^2-14n-11=3

Solution for 7n^2-14n-11=3 equation:

7n^2-14n-11=3

We move all terms to the left:

7n^2-14n-11-(3)=0

We add all the numbers together, and all the variables

7n^2-14n-14=0

a = 7; b = -14; c = -14;
Δ = b2-4ac
Δ = -142-4·7·(-14)
Δ = 588
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:

$\sqrt{\Delta}=\sqrt{588}=\sqrt{196*3}=\sqrt{196}*\sqrt{3}=14\sqrt{3}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-14\sqrt{3}}{2*7}=\frac{14-14\sqrt{3}}{14}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14\sqrt{3}}{2*7}=\frac{14+14\sqrt{3}}{14}
$