(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: 8)b!=0

b!=0/1

b!=0

b∈R



Domain of the equation: 4)b!=0

b!=0/1

b!=0

b∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

3b^2-b^2-3=0

We add all the numbers together, and all the variables

2b^2-3=0

a = 2; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·2·(-3)
Δ = 24
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{6}}{2*2}=\frac{0-2\sqrt{6}}{4}
=-\frac{2\sqrt{6}}{4}
=-\frac{\sqrt{6}}{2}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{6}}{2*2}=\frac{0+2\sqrt{6}}{4}
=\frac{2\sqrt{6}}{4}
=\frac{\sqrt{6}}{2}
$