30n^2-65n+25=0

Solution for 30n^2-65n+25=0 equation:

30n^2-65n+25=0

a = 30; b = -65; c = +25;
Δ = b2-4ac
Δ = -652-4·30·25
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-65)-35}{2*30}=\frac{30}{60}
=1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-65)+35}{2*30}=\frac{100}{60}
=1+2/3
$