35/x+8=21/3x

Solution for 35/x+8=21/3x equation:

35/x+8=21/3x

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

35/x-21/3x+8=0

We calculate fractions


105x/3x^2+(-21x)/3x^2+8=0

We multiply all the terms by the denominator


105x+(-21x)+8*3x^2=0

Wy multiply elements

24x^2+105x+(-21x)=0

We get rid of parentheses

24x^2+105x-21x=0

We add all the numbers together, and all the variables

24x^2+84x=0

a = 24; b = 84; c = 0;
Δ = b2-4ac
Δ = 842-4·24·0
Δ = 7056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7056}=84$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-84}{2*24}=\frac{-168}{48}
=-3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+84}{2*24}=\frac{0}{48}
=0
$