16n2-114n=-14

Solution for 16n2-114n=-14 equation:

16n^2-114n=-14

We move all terms to the left:

16n^2-114n-(-14)=0

We add all the numbers together, and all the variables

16n^2-114n+14=0

a = 16; b = -114; c = +14;
Δ = b2-4ac
Δ = -1142-4·16·14
Δ = 12100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12100}=110$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-114)-110}{2*16}=\frac{4}{32}
=1/8
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-114)+110}{2*16}=\frac{224}{32}
=7
$