5n^2-65=12n

Solution for 5n^2-65=12n equation:

5n^2-65=12n

We move all terms to the left:

5n^2-65-(12n)=0

a = 5; b = -12; c = -65;
Δ = b2-4ac
Δ = -122-4·5·(-65)
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-38}{2*5}=\frac{-26}{10}
=-2+3/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+38}{2*5}=\frac{50}{10}
=5
$