2-20/2b=2b/b+4

Solution for 2-20/2b=2b/b+4 equation:

2-20/2b=2b/b+4

We move all terms to the left:

2-20/2b-(2b/b+4)=0


Domain of the equation: 2b!=0

b!=0/2

b!=0

b∈R



Domain of the equation: b+4)!=0

b∈R


We get rid of parentheses

-20/2b-2b/b-4+2=0

We calculate fractions


(-4b^2)/2b^2+(-20b)/2b^2-4+2=0

We add all the numbers together, and all the variables

(-4b^2)/2b^2+(-20b)/2b^2-2=0

We multiply all the terms by the denominator


(-4b^2)+(-20b)-2*2b^2=0

Wy multiply elements

(-4b^2)-4b^2+(-20b)=0

We get rid of parentheses

-4b^2-4b^2-20b=0

We add all the numbers together, and all the variables

-8b^2-20b=0

a = -8; b = -20; c = 0;
Δ = b2-4ac
Δ = -202-4·(-8)·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20}{2*-8}=\frac{0}{-16}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20}{2*-8}=\frac{40}{-16}
=-2+1/2
$