0=-4.9x^2+13.1x+174.2

Solution for 0=-4.9x^2+13.1x+174.2 equation:

0=-4.9x^2+13.1x+174.2

We move all terms to the left:

0-(-4.9x^2+13.1x+174.2)=0

We add all the numbers together, and all the variables

-(-4.9x^2+13.1x+174.2)=0

We get rid of parentheses

4.9x^2-13.1x-174.2=0

a = 4.9; b = -13.1; c = -174.2;
Δ = b2-4ac
Δ = -13.12-4·4.9·(-174.2)
Δ = 3585.93
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{-(-13.1)-\sqrt{3585.93}}{2*4.9}=\frac{13.1-\sqrt{3585.93}}{9.8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13.1)+\sqrt{3585.93}}{2*4.9}=\frac{13.1+\sqrt{3585.93}}{9.8}
$