5n^2-n=13

Solution for 5n^2-n=13 equation:

5n^2-n=13

We move all terms to the left:

5n^2-n-(13)=0

We add all the numbers together, and all the variables

5n^2-1n-13=0

a = 5; b = -1; c = -13;
Δ = b2-4ac
Δ = -12-4·5·(-13)
Δ = 261
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{261}=\sqrt{9*29}=\sqrt{9}*\sqrt{29}=3\sqrt{29}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-3\sqrt{29}}{2*5}=\frac{1-3\sqrt{29}}{10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+3\sqrt{29}}{2*5}=\frac{1+3\sqrt{29}}{10}
$