2/3h-1/1h+11=8

Solution for 2/3h-1/1h+11=8 equation:

2/3h-1/1h+11=8

We move all terms to the left:

2/3h-1/1h+11-(8)=0


Domain of the equation: 3h!=0

h!=0/3

h!=0

h∈R



Domain of the equation: 1h!=0

h∈R


We add all the numbers together, and all the variables

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

We calculate fractions


2h/3h^2+(-3h)/3h^2+3=0

We multiply all the terms by the denominator


2h+(-3h)+3*3h^2=0

Wy multiply elements

9h^2+2h+(-3h)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

9h^2-1h=0

a = 9; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·9·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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