2/2b-5-4/b-3=0

Solution for 2/2b-5-4/b-3=0 equation:

2/2b-5-4/b-3=0


Domain of the equation: 2b!=0

b!=0/2

b!=0

b∈R



Domain of the equation: b!=0

b∈R


We add all the numbers together, and all the variables

2/2b-4/b-8=0

We calculate fractions


2b/2b^2+(-8b)/2b^2-8=0

We multiply all the terms by the denominator


2b+(-8b)-8*2b^2=0

Wy multiply elements

-16b^2+2b+(-8b)=0

We get rid of parentheses

-16b^2+2b-8b=0

We add all the numbers together, and all the variables

-16b^2-6b=0

a = -16; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·(-16)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*-16}=\frac{0}{-32}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*-16}=\frac{12}{-32}
=-3/8
$