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

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

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

We move all terms to the left:

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


Domain of the equation: 3h!=0

h!=0/3

h!=0

h∈R



Domain of the equation: 2h!=0

h!=0/2

h!=0

h∈R


We add all the numbers together, and all the variables

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

We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

18h^2+h=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{-2}{36}
=-1/18
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*18}=\frac{0}{36}
=0
$