1/3h-9=14h-7-13h

Solution for 1/3h-9=14h-7-13h equation:

1/3h-9=14h-7-13h

We move all terms to the left:

1/3h-9-(14h-7-13h)=0


Domain of the equation: 3h!=0

h!=0/3

h!=0

h∈R


We add all the numbers together, and all the variables

1/3h-(h-7)-9=0

We get rid of parentheses

1/3h-h+7-9=0

We multiply all the terms by the denominator


-h*3h+7*3h-9*3h+1=0

Wy multiply elements

-3h^2+21h-27h+1=0

We add all the numbers together, and all the variables

-3h^2-6h+1=0

a = -3; b = -6; c = +1;
Δ = b2-4ac
Δ = -62-4·(-3)·1
Δ = 48
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-4\sqrt{3}}{2*-3}=\frac{6-4\sqrt{3}}{-6}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+4\sqrt{3}}{2*-3}=\frac{6+4\sqrt{3}}{-6}
$