5n^2-n-3=3n^2-3

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

5n^2-n-3=3n^2-3

We move all terms to the left:

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

We add all the numbers together, and all the variables

5n^2-1n-(3n^2-3)-3=0

We get rid of parentheses

5n^2-3n^2-1n+3-3=0

We add all the numbers together, and all the variables

2n^2-1n=0

a = 2; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·2·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*2}=\frac{0}{4}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*2}=\frac{2}{4}
=1/2
$