216=1/3(36^2)h

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

216=1/3(36^2)h

We move all terms to the left:

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


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

h!=0/1

h!=0

h∈R


We get rid of parentheses

-1/336^2h+216=0

We multiply all the terms by the denominator


216*336^2h-1=0

Wy multiply elements

72576h^2-1=0

a = 72576; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·72576·(-1)
Δ = 290304
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:

$\sqrt{\Delta}=\sqrt{290304}=\sqrt{20736*14}=\sqrt{20736}*\sqrt{14}=144\sqrt{14}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-144\sqrt{14}}{2*72576}=\frac{0-144\sqrt{14}}{145152}
=-\frac{144\sqrt{14}}{145152}
=-\frac{\sqrt{14}}{1008}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+144\sqrt{14}}{2*72576}=\frac{0+144\sqrt{14}}{145152}
=\frac{144\sqrt{14}}{145152}
=\frac{\sqrt{14}}{1008}
$