-3/x+3/8x=21

Solution for -3/x+3/8x=21 equation:

-3/x+3/8x=21

We move all terms to the left:

-3/x+3/8x-(21)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We calculate fractions


(-24x)/8x^2+3x/8x^2-21=0

We multiply all the terms by the denominator


(-24x)+3x-21*8x^2=0

We add all the numbers together, and all the variables

3x+(-24x)-21*8x^2=0

Wy multiply elements

-168x^2+3x+(-24x)=0

We get rid of parentheses

-168x^2+3x-24x=0

We add all the numbers together, and all the variables

-168x^2-21x=0

a = -168; b = -21; c = 0;
Δ = b2-4ac
Δ = -212-4·(-168)·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-21}{2*-168}=\frac{0}{-336}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+21}{2*-168}=\frac{42}{-336}
=-1/8
$