120=-6x+4.9x^2

Solution for 120=-6x+4.9x^2 equation:

120=-6x+4.9x^2

We move all terms to the left:

120-(-6x+4.9x^2)=0

We get rid of parentheses

-4.9x^2+6x+120=0

a = -4.9; b = 6; c = +120;
Δ = b2-4ac
Δ = 62-4·(-4.9)·120
Δ = 2388
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:

$\sqrt{\Delta}=\sqrt{2388}=\sqrt{4*597}=\sqrt{4}*\sqrt{597}=2\sqrt{597}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{597}}{2*-4.9}=\frac{-6-2\sqrt{597}}{-9.8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{597}}{2*-4.9}=\frac{-6+2\sqrt{597}}{-9.8}
$