2/9h-1/3h+11=8

Solution for 2/9h-1/3h+11=8 equation:

2/9h-1/3h+11=8

We move all terms to the left:

2/9h-1/3h+11-(8)=0


Domain of the equation: 9h!=0

h!=0/9

h!=0

h∈R



Domain of the equation: 3h!=0

h!=0/3

h!=0

h∈R


We add all the numbers together, and all the variables

2/9h-1/3h+3=0

We calculate fractions


6h/27h^2+(-9h)/27h^2+3=0

We multiply all the terms by the denominator


6h+(-9h)+3*27h^2=0

Wy multiply elements

81h^2+6h+(-9h)=0

We get rid of parentheses

81h^2+6h-9h=0

We add all the numbers together, and all the variables

81h^2-3h=0

a = 81; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·81·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*81}=\frac{0}{162}
=0
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*81}=\frac{6}{162}
=1/27
$