3.14x^2=12000

Solution for 3.14x^2=12000 equation:

3.14x^2=12000

We move all terms to the left:

3.14x^2-(12000)=0

a = 3.14; b = 0; c = -12000;
Δ = b2-4ac
Δ = 02-4·3.14·(-12000)
Δ = 150720
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:

$\sqrt{\Delta}=\sqrt{150720}=\sqrt{64*2355}=\sqrt{64}*\sqrt{2355}=8\sqrt{2355}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{2355}}{2*3.14}=\frac{0-8\sqrt{2355}}{6.28}
=-\frac{8\sqrt{2355}}{6.28}
=-\frac{4\sqrt{2355}}{3.14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{2355}}{2*3.14}=\frac{0+8\sqrt{2355}}{6.28}
=\frac{8\sqrt{2355}}{6.28}
=\frac{4\sqrt{2355}}{3.14}
$