1/2y=2y+100

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

1/2y=2y+100

We move all terms to the left:

1/2y-(2y+100)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We get rid of parentheses

1/2y-2y-100=0

We multiply all the terms by the denominator


-2y*2y-100*2y+1=0

Wy multiply elements

-4y^2-200y+1=0

a = -4; b = -200; c = +1;
Δ = b2-4ac
Δ = -2002-4·(-4)·1
Δ = 40016
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{40016}=\sqrt{16*2501}=\sqrt{16}*\sqrt{2501}=4\sqrt{2501}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-4\sqrt{2501}}{2*-4}=\frac{200-4\sqrt{2501}}{-8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+4\sqrt{2501}}{2*-4}=\frac{200+4\sqrt{2501}}{-8}
$