21/4b+3/8b+1=11/8

Solution for 21/4b+3/8b+1=11/8 equation:

21/4b+3/8b+1=11/8

We move all terms to the left:

21/4b+3/8b+1-(11/8)=0


Domain of the equation: 4b!=0

b!=0/4

b!=0

b∈R



Domain of the equation: 8b!=0

b!=0/8

b!=0

b∈R


We add all the numbers together, and all the variables

21/4b+3/8b+1-(+11/8)=0

We get rid of parentheses

21/4b+3/8b+1-11/8=0

We calculate fractions


10752b/2048b^2+12b/2048b^2+(-44b)/2048b^2+1=0

We multiply all the terms by the denominator


10752b+12b+(-44b)+1*2048b^2=0

We add all the numbers together, and all the variables

10764b+(-44b)+1*2048b^2=0

Wy multiply elements

2048b^2+10764b+(-44b)=0

We get rid of parentheses

2048b^2+10764b-44b=0

We add all the numbers together, and all the variables

2048b^2+10720b=0

a = 2048; b = 10720; c = 0;
Δ = b2-4ac
Δ = 107202-4·2048·0
Δ = 114918400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{114918400}=10720$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10720)-10720}{2*2048}=\frac{-21440}{4096}
=-5+15/64
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10720)+10720}{2*2048}=\frac{0}{4096}
=0
$