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

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

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

We move all terms to the left:

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


Domain of the equation: 2h!=0

h!=0/2

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

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

We calculate fractions


3h/6h^2+(-4h)/6h^2+3=0

We multiply all the terms by the denominator


3h+(-4h)+3*6h^2=0

Wy multiply elements

18h^2+3h+(-4h)=0

We get rid of parentheses

18h^2+3h-4h=0

We add all the numbers together, and all the variables

18h^2-1h=0

a = 18; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·18·0
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*18}=\frac{0}{36}
=0
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*18}=\frac{2}{36}
=1/18
$