1/4b-5=2/5b-3

Solution for 1/4b-5=2/5b-3 equation:

1/4b-5=2/5b-3

We move all terms to the left:

1/4b-5-(2/5b-3)=0


Domain of the equation: 4b!=0

b!=0/4

b!=0

b∈R



Domain of the equation: 5b-3)!=0

b∈R


We get rid of parentheses

1/4b-2/5b+3-5=0

We calculate fractions


5b/20b^2+(-8b)/20b^2+3-5=0

We add all the numbers together, and all the variables

5b/20b^2+(-8b)/20b^2-2=0

We multiply all the terms by the denominator


5b+(-8b)-2*20b^2=0

Wy multiply elements

-40b^2+5b+(-8b)=0

We get rid of parentheses

-40b^2+5b-8b=0

We add all the numbers together, and all the variables

-40b^2-3b=0

a = -40; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-40)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*-40}=\frac{0}{-80}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-40}=\frac{6}{-80}
=-3/40
$