0=120+8x-4.9x^2

Solution for 0=120+8x-4.9x^2 equation:

0=120+8x-4.9x^2

We move all terms to the left:

0-(120+8x-4.9x^2)=0

We add all the numbers together, and all the variables

-(120+8x-4.9x^2)=0

We get rid of parentheses

4.9x^2-8x-120=0

a = 4.9; b = -8; c = -120;
Δ = b2-4ac
Δ = -82-4·4.9·(-120)
Δ = 2416
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2416}=\sqrt{16*151}=\sqrt{16}*\sqrt{151}=4\sqrt{151}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{151}}{2*4.9}=\frac{8-4\sqrt{151}}{9.8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{151}}{2*4.9}=\frac{8+4\sqrt{151}}{9.8}
$