1/2*3.14*x*100000000000x=1000

Solution for 1/2*3.14*x*100000000000x=1000 equation:

1/2*3.14x*100000000000x=1000

We move all terms to the left:

1/2*3.14x*100000000000x-(1000)=0


Domain of the equation: 2*3.14x*100000000000x!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


-1000*2*3.14x*100000000000x+1=0

Wy multiply elements

-600000000000000x^2*3+1=0

Wy multiply elements

-1800000000000000x^2+1=0

a = -1800000000000000; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-1800000000000000)·1
Δ = 7200000000000000
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:

$\sqrt{\Delta}=\sqrt{7200000000000000}=\sqrt{3600000000000000*2}=\sqrt{3600000000000000}*\sqrt{2}=60000000\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-60000000\sqrt{2}}{2*-1800000000000000}=\frac{0-60000000\sqrt{2}}{-3600000000000000}
=-\frac{60000000\sqrt{2}}{-3600000000000000}
=-\frac{\sqrt{2}}{-60000000}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+60000000\sqrt{2}}{2*-1800000000000000}=\frac{0+60000000\sqrt{2}}{-3600000000000000}
=\frac{60000000\sqrt{2}}{-3600000000000000}
=\frac{\sqrt{2}}{-60000000}
$