0=-4.9x^2+24.5x+1

Solution for 0=-4.9x^2+24.5x+1 equation:

0=-4.9x^2+24.5x+1

We move all terms to the left:

0-(-4.9x^2+24.5x+1)=0

We add all the numbers together, and all the variables

-(-4.9x^2+24.5x+1)=0

We get rid of parentheses

4.9x^2-24.5x-1=0

a = 4.9; b = -24.5; c = -1;
Δ = b2-4ac
Δ = -24.52-4·4.9·(-1)
Δ = 619.85
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{-(-24.5)-\sqrt{619.85}}{2*4.9}=\frac{24.5-\sqrt{619.85}}{9.8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24.5)+\sqrt{619.85}}{2*4.9}=\frac{24.5+\sqrt{619.85}}{9.8}
$