(3n+10)(3n-10)=n

Solution for (3n+10)(3n-10)=n equation:

(3n+10)(3n-10)=n

We move all terms to the left:

(3n+10)(3n-10)-(n)=0

We add all the numbers together, and all the variables

-1n+(3n+10)(3n-10)=0

We use the square of the difference formula

9n^2-1n-100=0

a = 9; b = -1; c = -100;
Δ = b2-4ac
Δ = -12-4·9·(-100)
Δ = 3601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{3601}}{2*9}=\frac{1-\sqrt{3601}}{18}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{3601}}{2*9}=\frac{1+\sqrt{3601}}{18}
$