4/x+7=2/3x

Solution for 4/x+7=2/3x equation:

4/x+7=2/3x

We move all terms to the left:

4/x+7-(2/3x)=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

4/x-(+2/3x)+7=0

We get rid of parentheses

4/x-2/3x+7=0

We calculate fractions


12x/3x^2+(-2x)/3x^2+7=0

We multiply all the terms by the denominator


12x+(-2x)+7*3x^2=0

Wy multiply elements

21x^2+12x+(-2x)=0

We get rid of parentheses

21x^2+12x-2x=0

We add all the numbers together, and all the variables

21x^2+10x=0

a = 21; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·21·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*21}=\frac{-20}{42}
=-10/21
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*21}=\frac{0}{42}
=0
$