3/4x-21/32x=-9/8

Solution for 3/4x-21/32x=-9/8 equation:

3/4x-21/32x=-9/8

We move all terms to the left:

3/4x-21/32x-(-9/8)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 32x!=0

x!=0/32

x!=0

x∈R


We get rid of parentheses

3/4x-21/32x+9/8=0

We calculate fractions


3456x^2/8192x^2+6144x/8192x^2+(-5376x)/8192x^2=0

We multiply all the terms by the denominator


3456x^2+6144x+(-5376x)=0

We get rid of parentheses

3456x^2+6144x-5376x=0

We add all the numbers together, and all the variables

3456x^2+768x=0

a = 3456; b = 768; c = 0;
Δ = b2-4ac
Δ = 7682-4·3456·0
Δ = 589824
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{589824}=768$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(768)-768}{2*3456}=\frac{-1536}{6912}
=-2/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(768)+768}{2*3456}=\frac{0}{6912}
=0
$