2/h+2h=9

Solution for 2/h+2h=9 equation:

2/h+2h=9

We move all terms to the left:

2/h+2h-(9)=0


Domain of the equation: h!=0

h∈R


We add all the numbers together, and all the variables

2h+2/h-9=0

We multiply all the terms by the denominator


2h*h-9*h+2=0

We add all the numbers together, and all the variables

-9h+2h*h+2=0

Wy multiply elements

2h^2-9h+2=0

a = 2; b = -9; c = +2;
Δ = b2-4ac
Δ = -92-4·2·2
Δ = 65
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{65}}{2*2}=\frac{9-\sqrt{65}}{4}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{65}}{2*2}=\frac{9+\sqrt{65}}{4}
$