-16x^2+45x+3.5=5.5

Solution for -16x^2+45x+3.5=5.5 equation:

-16x^2+45x+3.5=5.5

We move all terms to the left:

-16x^2+45x+3.5-(5.5)=0

We add all the numbers together, and all the variables

-16x^2+45x-2=0

a = -16; b = 45; c = -2;
Δ = b2-4ac
Δ = 452-4·(-16)·(-2)
Δ = 1897
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{-(45)-\sqrt{1897}}{2*-16}=\frac{-45-\sqrt{1897}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+\sqrt{1897}}{2*-16}=\frac{-45+\sqrt{1897}}{-32}
$