2=1/3h-3-3.4h

Solution for 2=1/3h-3-3.4h equation:

2=1/3h-3-3.4h

We move all terms to the left:

2-(1/3h-3-3.4h)=0


Domain of the equation: 3h-3-3.4h)!=0

We move all terms containing h to the left, all other terms to the right

3h-3.4h)!=3

h∈R


We add all the numbers together, and all the variables

-(-3.4h+1/3h-3)+2=0

We get rid of parentheses

3.4h-1/3h+3+2=0

We multiply all the terms by the denominator


(3.4h)*3h+3*3h+2*3h-1=0

We add all the numbers together, and all the variables

(+3.4h)*3h+3*3h+2*3h-1=0

We multiply parentheses

9h^2+3*3h+2*3h-1=0

Wy multiply elements

9h^2+9h+6h-1=0

We add all the numbers together, and all the variables

9h^2+15h-1=0

a = 9; b = 15; c = -1;
Δ = b2-4ac
Δ = 152-4·9·(-1)
Δ = 261
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:

$\sqrt{\Delta}=\sqrt{261}=\sqrt{9*29}=\sqrt{9}*\sqrt{29}=3\sqrt{29}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3\sqrt{29}}{2*9}=\frac{-15-3\sqrt{29}}{18}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3\sqrt{29}}{2*9}=\frac{-15+3\sqrt{29}}{18}
$