2/5b+1/4b=3

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

2/5b+1/4b=3

We move all terms to the left:

2/5b+1/4b-(3)=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 calculate fractions


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

We multiply all the terms by the denominator


8b+5b-3*20b^2=0

We add all the numbers together, and all the variables

13b-3*20b^2=0

Wy multiply elements

-60b^2+13b=0

a = -60; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-60)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*-60}=\frac{-26}{-120}
=13/60
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-60}=\frac{0}{-120}
=0
$