16x^2-28x-11=0

Solution for 16x^2-28x-11=0 equation:

16x^2-28x-11=0

a = 16; b = -28; c = -11;
Δ = b2-4ac
Δ = -282-4·16·(-11)
Δ = 1488
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:

$\sqrt{\Delta}=\sqrt{1488}=\sqrt{16*93}=\sqrt{16}*\sqrt{93}=4\sqrt{93}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-4\sqrt{93}}{2*16}=\frac{28-4\sqrt{93}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+4\sqrt{93}}{2*16}=\frac{28+4\sqrt{93}}{32}
$