10.5=-16x^2+111x+5.5

Solution for 10.5=-16x^2+111x+5.5 equation:

10.5=-16x^2+111x+5.5

We move all terms to the left:

10.5-(-16x^2+111x+5.5)=0

We get rid of parentheses

16x^2-111x-5.5+10.5=0

We add all the numbers together, and all the variables

16x^2-111x+5=0

a = 16; b = -111; c = +5;
Δ = b2-4ac
Δ = -1112-4·16·5
Δ = 12001
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{-(-111)-\sqrt{12001}}{2*16}=\frac{111-\sqrt{12001}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-111)+\sqrt{12001}}{2*16}=\frac{111+\sqrt{12001}}{32}
$