-16x^2+28x+5.5=5

Solution for -16x^2+28x+5.5=5 equation:

-16x^2+28x+5.5=5

We move all terms to the left:

-16x^2+28x+5.5-(5)=0

We add all the numbers together, and all the variables

-16x^2+28x+0.5=0

a = -16; b = 28; c = +0.5;
Δ = b2-4ac
Δ = 282-4·(-16)·0.5
Δ = 816
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:

$\sqrt{\Delta}=\sqrt{816}=\sqrt{16*51}=\sqrt{16}*\sqrt{51}=4\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-4\sqrt{51}}{2*-16}=\frac{-28-4\sqrt{51}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+4\sqrt{51}}{2*-16}=\frac{-28+4\sqrt{51}}{-32}
$