H(0)=-4.9x^2-+8x+5

Solution for H(0)=-4.9x^2-+8x+5 equation:

(0)=-4.9H^2-+8H+5

We move all terms to the left:

(0)-(-4.9H^2-+8H+5)=0

We add all the numbers together, and all the variables

-(-4.9H^2-+8H+5)=0

We use the square of the difference formula

-(-4.9H^2-8H+5)=0

We get rid of parentheses

4.9H^2+8H-5=0

a = 4.9; b = 8; c = -5;
Δ = b2-4ac
Δ = 82-4·4.9·(-5)
Δ = 162
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{162}=\sqrt{81*2}=\sqrt{81}*\sqrt{2}=9\sqrt{2}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-9\sqrt{2}}{2*4.9}=\frac{-8-9\sqrt{2}}{9.8}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+9\sqrt{2}}{2*4.9}=\frac{-8+9\sqrt{2}}{9.8}
$