1/3h+8=1/6h+13

Solution for 1/3h+8=1/6h+13 equation:

1/3h+8=1/6h+13

We move all terms to the left:

1/3h+8-(1/6h+13)=0


Domain of the equation: 3h!=0

h!=0/3

h!=0

h∈R



Domain of the equation: 6h+13)!=0

h∈R


We get rid of parentheses

1/3h-1/6h-13+8=0

We calculate fractions


6h/18h^2+(-3h)/18h^2-13+8=0

We add all the numbers together, and all the variables

6h/18h^2+(-3h)/18h^2-5=0

We multiply all the terms by the denominator


6h+(-3h)-5*18h^2=0

Wy multiply elements

-90h^2+6h+(-3h)=0

We get rid of parentheses

-90h^2+6h-3h=0

We add all the numbers together, and all the variables

-90h^2+3h=0

a = -90; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-90)·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*-90}=\frac{-6}{-180}
=1/30
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-90}=\frac{0}{-180}
=0
$