5n^2-13=10n

Solution for 5n^2-13=10n equation:

5n^2-13=10n

We move all terms to the left:

5n^2-13-(10n)=0

a = 5; b = -10; c = -13;
Δ = b2-4ac
Δ = -102-4·5·(-13)
Δ = 360
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:

$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-6\sqrt{10}}{2*5}=\frac{10-6\sqrt{10}}{10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+6\sqrt{10}}{2*5}=\frac{10+6\sqrt{10}}{10}
$