7n^2-6=n

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

7n^2-6=n

We move all terms to the left:

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

We add all the numbers together, and all the variables

7n^2-1n-6=0

a = 7; b = -1; c = -6;
Δ = b2-4ac
Δ = -12-4·7·(-6)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-13}{2*7}=\frac{-12}{14}
=-6/7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+13}{2*7}=\frac{14}{14}
=1
$