1/3h-3h=-6

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

1/3h-3h=-6

We move all terms to the left:

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


Domain of the equation: 3h!=0

h!=0/3

h!=0

h∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-9h^2+18h+1=0

a = -9; b = 18; c = +1;
Δ = b2-4ac
Δ = 182-4·(-9)·1
Δ = 360
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:

$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-6\sqrt{10}}{2*-9}=\frac{-18-6\sqrt{10}}{-18}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+6\sqrt{10}}{2*-9}=\frac{-18+6\sqrt{10}}{-18}
$