5n^2-3=n

Solution for 5n^2-3=n equation:

5n^2-3=n

We move all terms to the left:

5n^2-3-(n)=0

We add all the numbers together, and all the variables

5n^2-1n-3=0

a = 5; b = -1; c = -3;
Δ = b2-4ac
Δ = -12-4·5·(-3)
Δ = 61
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{61}}{2*5}=\frac{1-\sqrt{61}}{10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{61}}{2*5}=\frac{1+\sqrt{61}}{10}
$