1/2h-2/3h=1/2(9-1)

Solution for 1/2h-2/3h=1/2(9-1) equation:

1/2h-2/3h=1/2(9-1)

We move all terms to the left:

1/2h-2/3h-(1/2(9-1))=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-(1/28)=0

We get rid of parentheses

1/2h-2/3h-1/28=0

We calculate fractions


(-18h^2)/336h^2+168h/336h^2+(-224h)/336h^2=0

We multiply all the terms by the denominator


(-18h^2)+168h+(-224h)=0

We get rid of parentheses

-18h^2+168h-224h=0

We add all the numbers together, and all the variables

-18h^2-56h=0

a = -18; b = -56; c = 0;
Δ = b2-4ac
Δ = -562-4·(-18)·0
Δ = 3136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3136}=56$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-56}{2*-18}=\frac{0}{-36}
=0
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+56}{2*-18}=\frac{112}{-36}
=-3+1/9
$