6n^2-30n+28=0

Solution for 6n^2-30n+28=0 equation:

6n^2-30n+28=0

a = 6; b = -30; c = +28;
Δ = b2-4ac
Δ = -302-4·6·28
Δ = 228
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:

$\sqrt{\Delta}=\sqrt{228}=\sqrt{4*57}=\sqrt{4}*\sqrt{57}=2\sqrt{57}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{57}}{2*6}=\frac{30-2\sqrt{57}}{12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{57}}{2*6}=\frac{30+2\sqrt{57}}{12}
$