5n^2-128=12n

Solution for 5n^2-128=12n equation:

5n^2-128=12n

We move all terms to the left:

5n^2-128-(12n)=0

a = 5; b = -12; c = -128;
Δ = b2-4ac
Δ = -122-4·5·(-128)
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-52}{2*5}=\frac{-40}{10}
=-4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+52}{2*5}=\frac{64}{10}
=6+2/5
$