30n^2-128n+128=0

Solution for 30n^2-128n+128=0 equation:

30n^2-128n+128=0

a = 30; b = -128; c = +128;
Δ = b2-4ac
Δ = -1282-4·30·128
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-128)-32}{2*30}=\frac{96}{60}
=1+3/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-128)+32}{2*30}=\frac{160}{60}
=2+2/3
$