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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We calculate fractions


168b/512b^2+192b/512b^2+88b/512b^2-4=0

We multiply all the terms by the denominator


168b+192b+88b-4*512b^2=0

We add all the numbers together, and all the variables

448b-4*512b^2=0

Wy multiply elements

-2048b^2+448b=0

a = -2048; b = 448; c = 0;
Δ = b2-4ac
Δ = 4482-4·(-2048)·0
Δ = 200704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{200704}=448$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(448)-448}{2*-2048}=\frac{-896}{-4096}
=7/32
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(448)+448}{2*-2048}=\frac{0}{-4096}
=0
$