200/3.14=r2

Solution for 200/3.14=r2 equation:

200/3.14=r2

We move all terms to the left:

200/3.14-(r2)=0

We add all the numbers together, and all the variables

-1r^2+200/3.14=0

We multiply all the terms by the denominator


-1r^2*3.14+200=0

Wy multiply elements

-3.14r^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:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2512}=\sqrt{16*157}=\sqrt{16}*\sqrt{157}=4\sqrt{157}$
$r_{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}
$
$r_{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}
$