150^3=1/3*3,14*4^2*h

Solution for 150^3=1/3*3,14*4^2*h equation:

150^3=1/3*3.14*4^2h

We move all terms to the left:

150^3-(1/3*3.14*4^2h)=0


Domain of the equation: 3*3.14*4^2h)!=0

h!=0/1

h!=0

h∈R


We add all the numbers together, and all the variables

-(1/3*3.14*4^2h)+3375000=0

We get rid of parentheses

-1/3*3.14*4^2h+3375000=0

We multiply all the terms by the denominator


3375000*3*3.14*4^2h-1=0

Wy multiply elements

127170000h^2*3-1=0

Wy multiply elements

381510000h^2-1=0

a = 381510000; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·381510000·(-1)
Δ = 1526040000
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:

$\sqrt{\Delta}=\sqrt{1526040000}=\sqrt{3240000*471}=\sqrt{3240000}*\sqrt{471}=1800\sqrt{471}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-1800\sqrt{471}}{2*381510000}=\frac{0-1800\sqrt{471}}{763020000}
=-\frac{1800\sqrt{471}}{763020000}
=-\frac{\sqrt{471}}{423900}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+1800\sqrt{471}}{2*381510000}=\frac{0+1800\sqrt{471}}{763020000}
=\frac{1800\sqrt{471}}{763020000}
=\frac{\sqrt{471}}{423900}
$