((4/3)*3.14159265359*(1.2+0.01x)^3)-(4/3*3.141592653594*(1.2)^3)=1980/2700

Solution for ((4/3)*3.14159265359*(1.2+0.01x)^3)-(4/3*3.141592653594*(1.2)^3)=1980/2700 equation:

((4/3)*3.14159265359(1.2+0.01x)^3)-(4/3*3.141592653594(1.2)^3)=1980/2700

We move all terms to the left:

((4/3)*3.14159265359(1.2+0.01x)^3)-(4/3*3.141592653594(1.2)^3)-(1980/2700)=0


Domain of the equation: 3)*3.14159265359(1.2+0.01x)^3)!=0

x∈R


We add all the numbers together, and all the variables

((+4/3)*3.14159265359(0.01x+1.2)^3)-(4/3*3.141592653594(1.2)^3)-(+1980/2700)=0

We get rid of parentheses

((+4/3)*3.14159265359(0.01x+1.2)^3)-(4/3*3.141592653594(1.2)^3)-1980/2700=0

We calculate fractions


(-17820x^2)/3*3.14159265359(0.01x)+()/3*3.14159265359(0.01x)+(-97200x)/3*3.14159265359(0.01x)=0

We add all the numbers together, and all the variables

(-17820x^2)/3*3.14159265359(+0.01x)+()/3*3.14159265359(+0.01x)+(-97200x)/3*3.14159265359(+0.01x)=0

We multiply all the terms by the denominator


(-17820x^2)+(-97200x)+()=0

We add all the numbers together, and all the variables

(-17820x^2)+(-97200x)=0

We get rid of parentheses

-17820x^2-97200x=0

a = -17820; b = -97200; c = 0;
Δ = b2-4ac
Δ = -972002-4·(-17820)·0
Δ = 9447840000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9447840000}=97200$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-97200)-97200}{2*-17820}=\frac{0}{-35640}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-97200)+97200}{2*-17820}=\frac{194400}{-35640}
=-5+5/11
$