200=(3x)(3.14x^2)

Solution for 200=(3x)(3.14x^2) equation:

200=(3x)(3.14x^2)

We move all terms to the left:

200-((3x)(3.14x^2))=0


We calculate terms in parentheses: -(3x(3.14x^2)), so:

3x(3.14x^2)

We multiply parentheses

9x^2

Back to the equation:

-(9x^2)


a = -9; b = 0; c = +200;
Δ = b2-4ac
Δ = 02-4·(-9)·200
Δ = 7200
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{7200}=\sqrt{3600*2}=\sqrt{3600}*\sqrt{2}=60\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-60\sqrt{2}}{2*-9}=\frac{0-60\sqrt{2}}{-18}
=-\frac{60\sqrt{2}}{-18}
=-\frac{10\sqrt{2}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+60\sqrt{2}}{2*-9}=\frac{0+60\sqrt{2}}{-18}
=\frac{60\sqrt{2}}{-18}
=\frac{10\sqrt{2}}{-3}
$