9n^2-13=5n

Solution for 9n^2-13=5n equation:

9n^2-13=5n

We move all terms to the left:

9n^2-13-(5n)=0

a = 9; b = -5; c = -13;
Δ = b2-4ac
Δ = -52-4·9·(-13)
Δ = 493
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{-(-5)-\sqrt{493}}{2*9}=\frac{5-\sqrt{493}}{18}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{493}}{2*9}=\frac{5+\sqrt{493}}{18}
$