1/4b=-3/8b+5

Solution for 1/4b=-3/8b+5 equation:

1/4b=-3/8b+5

We move all terms to the left:

1/4b-(-3/8b+5)=0


Domain of the equation: 4b!=0

b!=0/4

b!=0

b∈R



Domain of the equation: 8b+5)!=0

b∈R


We get rid of parentheses

1/4b+3/8b-5=0

We calculate fractions


8b/32b^2+12b/32b^2-5=0

We multiply all the terms by the denominator


8b+12b-5*32b^2=0

We add all the numbers together, and all the variables

20b-5*32b^2=0

Wy multiply elements

-160b^2+20b=0

a = -160; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·(-160)·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*-160}=\frac{-40}{-320}
=1/8
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*-160}=\frac{0}{-320}
=0
$