1/2X+10=100y

Solution for 1/2X+10=100y equation:

1/2X+10=100X

We move all terms to the left:

1/2X+10-(100X)=0


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We add all the numbers together, and all the variables

-100X+1/2X+10=0

We multiply all the terms by the denominator


-100X*2X+10*2X+1=0

Wy multiply elements

-200X^2+20X+1=0

a = -200; b = 20; c = +1;
Δ = b2-4ac
Δ = 202-4·(-200)·1
Δ = 1200
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:

$\sqrt{\Delta}=\sqrt{1200}=\sqrt{400*3}=\sqrt{400}*\sqrt{3}=20\sqrt{3}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20\sqrt{3}}{2*-200}=\frac{-20-20\sqrt{3}}{-400}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20\sqrt{3}}{2*-200}=\frac{-20+20\sqrt{3}}{-400}
$