16x^2-44x+9=0

Solution for 16x^2-44x+9=0 equation:

16x^2-44x+9=0

a = 16; b = -44; c = +9;
Δ = b2-4ac
Δ = -442-4·16·9
Δ = 1360
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:

$\sqrt{\Delta}=\sqrt{1360}=\sqrt{16*85}=\sqrt{16}*\sqrt{85}=4\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-4\sqrt{85}}{2*16}=\frac{44-4\sqrt{85}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+4\sqrt{85}}{2*16}=\frac{44+4\sqrt{85}}{32}
$