16n^2-114n+4=0

Solution for 16n^2-114n+4=0 equation:

16n^2-114n+4=0

a = 16; b = -114; c = +4;
Δ = b2-4ac
Δ = -1142-4·16·4
Δ = 12740
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:

$\sqrt{\Delta}=\sqrt{12740}=\sqrt{196*65}=\sqrt{196}*\sqrt{65}=14\sqrt{65}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-114)-14\sqrt{65}}{2*16}=\frac{114-14\sqrt{65}}{32}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-114)+14\sqrt{65}}{2*16}=\frac{114+14\sqrt{65}}{32}
$