360^3=1/3*72^2*h

Solution for 360^3=1/3*72^2*h equation:

360^3=1/3*72^2h

We move all terms to the left:

360^3-(1/3*72^2h)=0


Domain of the equation: 3*72^2h)!=0

h!=0/1

h!=0

h∈R


We add all the numbers together, and all the variables

-(1/3*72^2h)+46656000=0

We get rid of parentheses

-1/3*72^2h+46656000=0

We multiply all the terms by the denominator


46656000*3*72^2h-1=0

Wy multiply elements

10077696000h^2*7-1=0

Wy multiply elements

70543872000h^2-1=0

a = 70543872000; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·70543872000·(-1)
Δ = 282175488000
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:

$\sqrt{\Delta}=\sqrt{282175488000}=\sqrt{2687385600*105}=\sqrt{2687385600}*\sqrt{105}=51840\sqrt{105}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-51840\sqrt{105}}{2*70543872000}=\frac{0-51840\sqrt{105}}{141087744000}
=-\frac{51840\sqrt{105}}{141087744000}
=-\frac{\sqrt{105}}{2721600}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+51840\sqrt{105}}{2*70543872000}=\frac{0+51840\sqrt{105}}{141087744000}
=\frac{51840\sqrt{105}}{141087744000}
=\frac{\sqrt{105}}{2721600}
$