216^3=1/3(36^2)h

Solution for 216^3=1/3(36^2)h equation:

216^3=1/3(36^2)h

We move all terms to the left:

216^3-(1/3(36^2)h)=0


Domain of the equation: 336^2h)!=0

h!=0/1

h!=0

h∈R


We add all the numbers together, and all the variables

-(1/336^2h)+10077696=0

We get rid of parentheses

-1/336^2h+10077696=0

We multiply all the terms by the denominator


10077696*336^2h-1=0

Wy multiply elements

3386105856h^2-1=0

a = 3386105856; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·3386105856·(-1)
Δ = 13544423424
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:

$\sqrt{\Delta}=\sqrt{13544423424}=\sqrt{967458816*14}=\sqrt{967458816}*\sqrt{14}=31104\sqrt{14}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-31104\sqrt{14}}{2*3386105856}=\frac{0-31104\sqrt{14}}{6772211712}
=-\frac{31104\sqrt{14}}{6772211712}
=-\frac{\sqrt{14}}{217728}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+31104\sqrt{14}}{2*3386105856}=\frac{0+31104\sqrt{14}}{6772211712}
=\frac{31104\sqrt{14}}{6772211712}
=\frac{\sqrt{14}}{217728}
$