5/b+10=2/2b+4

Solution for 5/b+10=2/2b+4 equation:

5/b+10=2/2b+4

We move all terms to the left:

5/b+10-(2/2b+4)=0


Domain of the equation: b!=0

b∈R



Domain of the equation: 2b+4)!=0

b∈R


We get rid of parentheses

5/b-2/2b-4+10=0

We calculate fractions


10b/2b^2+(-2b)/2b^2-4+10=0

We add all the numbers together, and all the variables

10b/2b^2+(-2b)/2b^2+6=0

We multiply all the terms by the denominator


10b+(-2b)+6*2b^2=0

Wy multiply elements

12b^2+10b+(-2b)=0

We get rid of parentheses

12b^2+10b-2b=0

We add all the numbers together, and all the variables

12b^2+8b=0

a = 12; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·12·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*12}=\frac{-16}{24}
=-2/3
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*12}=\frac{0}{24}
=0
$