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

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

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

We move all terms to the left:

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

We get rid of parentheses

16x^2-5x-5.5x+x=0

We add all the numbers together, and all the variables

16x^2-9.5x=0

a = 16; b = -9.5; c = 0;
Δ = b2-4ac
Δ = -9.52-4·16·0
Δ = 90.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9.5)-\sqrt{90.25}}{2*16}=\frac{9.5-\sqrt{90.25}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9.5)+\sqrt{90.25}}{2*16}=\frac{9.5+\sqrt{90.25}}{32}
$