16x^2-40x-23=0

Solution for 16x^2-40x-23=0 equation:

16x^2-40x-23=0

a = 16; b = -40; c = -23;
Δ = b2-4ac
Δ = -402-4·16·(-23)
Δ = 3072
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:

$\sqrt{\Delta}=\sqrt{3072}=\sqrt{1024*3}=\sqrt{1024}*\sqrt{3}=32\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-32\sqrt{3}}{2*16}=\frac{40-32\sqrt{3}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+32\sqrt{3}}{2*16}=\frac{40+32\sqrt{3}}{32}
$