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

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

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

We move all terms to the left:

3/2h-1/3h+1-(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

3/2h-1/3h-7=0

We calculate fractions


9h/6h^2+(-2h)/6h^2-7=0

We multiply all the terms by the denominator


9h+(-2h)-7*6h^2=0

Wy multiply elements

-42h^2+9h+(-2h)=0

We get rid of parentheses

-42h^2+9h-2h=0

We add all the numbers together, and all the variables

-42h^2+7h=0

a = -42; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-42)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-42}=\frac{-14}{-84}
=1/6
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-42}=\frac{0}{-84}
=0
$