2n^2-15=n

Solution for 2n^2-15=n equation:

2n^2-15=n

We move all terms to the left:

2n^2-15-(n)=0

We add all the numbers together, and all the variables

2n^2-1n-15=0

a = 2; b = -1; c = -15;
Δ = b2-4ac
Δ = -12-4·2·(-15)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-11}{2*2}=\frac{-10}{4}
=-2+1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+11}{2*2}=\frac{12}{4}
=3
$