3.14x^2=20000

Solution for 3.14x^2=20000 equation:

3.14x^2=20000

We move all terms to the left:

3.14x^2-(20000)=0

a = 3.14; b = 0; c = -20000;
Δ = b2-4ac
Δ = 02-4·3.14·(-20000)
Δ = 251200
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:

$\sqrt{\Delta}=\sqrt{251200}=\sqrt{1600*157}=\sqrt{1600}*\sqrt{157}=40\sqrt{157}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{157}}{2*3.14}=\frac{0-40\sqrt{157}}{6.28}
=-\frac{40\sqrt{157}}{6.28}
=-\frac{20\sqrt{157}}{3.14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{157}}{2*3.14}=\frac{0+40\sqrt{157}}{6.28}
=\frac{40\sqrt{157}}{6.28}
=\frac{20\sqrt{157}}{3.14}
$