0=115+12.25k-4.9k^2

Solution for 0=115+12.25k-4.9k^2 equation:

0=115+12.25k-4.9k^2

We move all terms to the left:

0-(115+12.25k-4.9k^2)=0

We add all the numbers together, and all the variables

-(115+12.25k-4.9k^2)=0

We get rid of parentheses

4.9k^2-12.25k-115=0

a = 4.9; b = -12.25; c = -115;
Δ = b2-4ac
Δ = -12.252-4·4.9·(-115)
Δ = 2404.0625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12.25)-\sqrt{2404.0625}}{2*4.9}=\frac{12.25-\sqrt{2404.0625}}{9.8}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12.25)+\sqrt{2404.0625}}{2*4.9}=\frac{12.25+\sqrt{2404.0625}}{9.8}
$