h=0.5/9.80.64

Solution for h=0.5/9.80.64 equation:

h=0.5/9.80.64

We move all terms to the left:

h-(0.5/9.80.64)=0

We add all the numbers together, and all the variables

h-(+0.5/9.80.64)=0

We get rid of parentheses

h-0.5/9.80.64=0

We multiply all the terms by the denominator


h*9.80.64-0.5=0

Wy multiply elements

9h^2-0.5=0

a = 9; b = 0; c = -0.5;
Δ = b2-4ac
Δ = 02-4·9·(-0.5)
Δ = 18
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:

$\sqrt{\Delta}=\sqrt{18}=\sqrt{9*2}=\sqrt{9}*\sqrt{2}=3\sqrt{2}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-3\sqrt{2}}{2*9}=\frac{0-3\sqrt{2}}{18}
=-\frac{3\sqrt{2}}{18}
=-\frac{\sqrt{2}}{6}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+3\sqrt{2}}{2*9}=\frac{0+3\sqrt{2}}{18}
=\frac{3\sqrt{2}}{18}
=\frac{\sqrt{2}}{6}
$