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

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

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

We move all terms to the left:

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

We get rid of parentheses

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}
$