2/5b-1/4b=3*20

Solution for 2/5b-1/4b=3*20 equation:

2/5b-1/4b=3*20

We move all terms to the left:

2/5b-1/4b-(3*20)=0


Domain of the equation: 5b!=0

b!=0/5

b!=0

b∈R



Domain of the equation: 4b!=0

b!=0/4

b!=0

b∈R


We add all the numbers together, and all the variables

2/5b-1/4b-60=0

We calculate fractions


8b/20b^2+(-5b)/20b^2-60=0

We multiply all the terms by the denominator


8b+(-5b)-60*20b^2=0

Wy multiply elements

-1200b^2+8b+(-5b)=0

We get rid of parentheses

-1200b^2+8b-5b=0

We add all the numbers together, and all the variables

-1200b^2+3b=0

a = -1200; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-1200)·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*-1200}=\frac{-6}{-2400}
=1/400
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-1200}=\frac{0}{-2400}
=0
$