3.14x^2=200

Solution for 3.14x^2=200 equation:

3.14x^2=200

We move all terms to the left:

3.14x^2-(200)=0

a = 3.14; b = 0; c = -200;
Δ = b2-4ac
Δ = 02-4·3.14·(-200)
Δ = 2512
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:

$\sqrt{\Delta}=\sqrt{2512}=\sqrt{16*157}=\sqrt{16}*\sqrt{157}=4\sqrt{157}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{157}}{2*3.14}=\frac{0-4\sqrt{157}}{6.28}
=-\frac{4\sqrt{157}}{6.28}
=-\frac{2\sqrt{157}}{3.14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{157}}{2*3.14}=\frac{0+4\sqrt{157}}{6.28}
=\frac{4\sqrt{157}}{6.28}
=\frac{2\sqrt{157}}{3.14}
$