v=4/3*3.14*(83)^3

Solution for v=4/3*3.14*(83)^3 equation:

v=4/3*3.14(83)^3

We move all terms to the left:

v-(4/3*3.14(83)^3)=0

We get rid of parentheses

v-4/3*3.1483^3=0

We multiply all the terms by the denominator


v*3*3.1483^3-4=0

Wy multiply elements

9v^2*3-4=0

Wy multiply elements

27v^2-4=0

a = 27; b = 0; c = -4;
Δ = b2-4ac
Δ = 02-4·27·(-4)
Δ = 432
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{3}}{2*27}=\frac{0-12\sqrt{3}}{54}
=-\frac{12\sqrt{3}}{54}
=-\frac{2\sqrt{3}}{9}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{3}}{2*27}=\frac{0+12\sqrt{3}}{54}
=\frac{12\sqrt{3}}{54}
=\frac{2\sqrt{3}}{9}
$