0=150-4.9x^2-2x

Solution for 0=150-4.9x^2-2x equation:

0=150-4.9x^2-2x

We move all terms to the left:

0-(150-4.9x^2-2x)=0

We add all the numbers together, and all the variables

-(150-4.9x^2-2x)=0

We get rid of parentheses

4.9x^2+2x-150=0

a = 4.9; b = 2; c = -150;
Δ = b2-4ac
Δ = 22-4·4.9·(-150)
Δ = 2944
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:

$\sqrt{\Delta}=\sqrt{2944}=\sqrt{64*46}=\sqrt{64}*\sqrt{46}=8\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-8\sqrt{46}}{2*4.9}=\frac{-2-8\sqrt{46}}{9.8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+8\sqrt{46}}{2*4.9}=\frac{-2+8\sqrt{46}}{9.8}
$