(7x/x-2)-(5/3-x)=0

Solution for (7x/x-2)-(5/3-x)=0 equation:

(7x/x-2)-(5/3-x)=0


Domain of the equation: x-2)!=0

x∈R



Domain of the equation: 3-x)!=0

We move all terms containing x to the left, all other terms to the right

-x)!=-3

x!=-3/1

x!=-3

x∈R


We add all the numbers together, and all the variables

(7x/x-2)-(-1x+5/3)=0

We get rid of parentheses

7x/x+1x-2-5/3=0

We calculate fractions


1x+21x/3x+(-5x)/3x-2=0

We add all the numbers together, and all the variables

x+21x/3x+(-5x)/3x-2=0

We multiply all the terms by the denominator


x*3x+21x+(-5x)-2*3x=0

We add all the numbers together, and all the variables

21x+x*3x+(-5x)-2*3x=0

Wy multiply elements

3x^2+21x+(-5x)-6x=0

We get rid of parentheses

3x^2+21x-5x-6x=0

We add all the numbers together, and all the variables

3x^2+10x=0

a = 3; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·3·0
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*3}=\frac{-20}{6}
=-3+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*3}=\frac{0}{6}
=0
$