1/3h-6h=2

Solution for 1/3h-6h=2 equation:

1/3h-6h=2

We move all terms to the left:

1/3h-6h-(2)=0


Domain of the equation: 3h!=0

h!=0/3

h!=0

h∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-18h^2-6h+1=0

a = -18; b = -6; c = +1;
Δ = b2-4ac
Δ = -62-4·(-18)·1
Δ = 108
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:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{3}}{2*-18}=\frac{6-6\sqrt{3}}{-36}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{3}}{2*-18}=\frac{6+6\sqrt{3}}{-36}
$