3/8(b)-1/4(b)=3

Solution for 3/8(b)-1/4(b)=3 equation:

3/8(b)-1/4(b)=3

We move all terms to the left:

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


Domain of the equation: 8b!=0

b!=0/8

b!=0

b∈R



Domain of the equation: 4b!=0

b!=0/4

b!=0

b∈R


We calculate fractions


12b/32b^2+(-8b)/32b^2-3=0

We multiply all the terms by the denominator


12b+(-8b)-3*32b^2=0

Wy multiply elements

-96b^2+12b+(-8b)=0

We get rid of parentheses

-96b^2+12b-8b=0

We add all the numbers together, and all the variables

-96b^2+4b=0

a = -96; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-96)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*-96}=\frac{-8}{-192}
=1/24
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-96}=\frac{0}{-192}
=0
$