29=-4.9x^2+33.8x+45

Solution for 29=-4.9x^2+33.8x+45 equation:

29=-4.9x^2+33.8x+45

We move all terms to the left:

29-(-4.9x^2+33.8x+45)=0

We get rid of parentheses

4.9x^2-33.8x-45+29=0

We add all the numbers together, and all the variables

4.9x^2-33.8x-16=0

a = 4.9; b = -33.8; c = -16;
Δ = b2-4ac
Δ = -33.82-4·4.9·(-16)
Δ = 1456.04
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{-(-33.8)-\sqrt{1456.04}}{2*4.9}=\frac{33.8-\sqrt{1456.04}}{9.8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33.8)+\sqrt{1456.04}}{2*4.9}=\frac{33.8+\sqrt{1456.04}}{9.8}
$