21/4*x+1/8+7/8*x=1/16

Solution for 21/4*x+1/8+7/8*x=1/16 equation:

21/4x+1/8+7/8x=1/16

We move all terms to the left:

21/4x+1/8+7/8x-(1/16)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

21/4x+7/8x+1/8-(+1/16)=0

We get rid of parentheses

21/4x+7/8x+1/8-1/16=0

We calculate fractions


(-2048x^2)/32768x^2+172032x/32768x^2+448x/32768x^2+64x/32768x^2=0

We multiply all the terms by the denominator


(-2048x^2)+172032x+448x+64x=0

We add all the numbers together, and all the variables

(-2048x^2)+172544x=0

We get rid of parentheses

-2048x^2+172544x=0

a = -2048; b = 172544; c = 0;
Δ = b2-4ac
Δ = 1725442-4·(-2048)·0
Δ = 29771431936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{29771431936}=172544$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(172544)-172544}{2*-2048}=\frac{-345088}{-4096}
=84+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(172544)+172544}{2*-2048}=\frac{0}{-4096}
=0
$