4.5=3x+4.9x^2

Solution for 4.5=3x+4.9x^2 equation:

4.5=3x+4.9x^2

We move all terms to the left:

4.5-(3x+4.9x^2)=0

We get rid of parentheses

-4.9x^2-3x+4.5=0

a = -4.9; b = -3; c = +4.5;
Δ = b2-4ac
Δ = -32-4·(-4.9)·4.5
Δ = 97.2
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{-(-3)-\sqrt{97.2}}{2*-4.9}=\frac{3-\sqrt{97.2}}{-9.8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{97.2}}{2*-4.9}=\frac{3+\sqrt{97.2}}{-9.8}
$