0.5=0+3.13x+4.9x^2

Solution for 0.5=0+3.13x+4.9x^2 equation:

0.5=0+3.13x+4.9x^2

We move all terms to the left:

0.5-(0+3.13x+4.9x^2)=0

We get rid of parentheses

-4.9x^2-3.13x-0+0.5=0

We add all the numbers together, and all the variables

-4.9x^2-3.13x+0.5=0

a = -4.9; b = -3.13; c = +0.5;
Δ = b2-4ac
Δ = -3.132-4·(-4.9)·0.5
Δ = 19.5969
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{-(-3.13)-\sqrt{19.5969}}{2*-4.9}=\frac{3.13-\sqrt{19.5969}}{-9.8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3.13)+\sqrt{19.5969}}{2*-4.9}=\frac{3.13+\sqrt{19.5969}}{-9.8}
$