16x^2-114x+199=0

Solution for 16x^2-114x+199=0 equation:

16x^2-114x+199=0

a = 16; b = -114; c = +199;
Δ = b2-4ac
Δ = -1142-4·16·199
Δ = 260
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{260}=\sqrt{4*65}=\sqrt{4}*\sqrt{65}=2\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-114)-2\sqrt{65}}{2*16}=\frac{114-2\sqrt{65}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-114)+2\sqrt{65}}{2*16}=\frac{114+2\sqrt{65}}{32}
$