7/3x+1/2x=10+5/3x

Solution for 7/3x+1/2x=10+5/3x equation:

7/3x+1/2x=10+5/3x

We move all terms to the left:

7/3x+1/2x-(10+5/3x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

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

7/3x+1/2x-(5/3x+10)=0

We get rid of parentheses

7/3x+1/2x-5/3x-10=0

We calculate fractions


(-10x+7)/6x^2+3x/6x^2-10=0

We multiply all the terms by the denominator


(-10x+7)+3x-10*6x^2=0

We add all the numbers together, and all the variables

3x+(-10x+7)-10*6x^2=0

Wy multiply elements

-60x^2+3x+(-10x+7)=0

We get rid of parentheses

-60x^2+3x-10x+7=0

We add all the numbers together, and all the variables

-60x^2-7x+7=0

a = -60; b = -7; c = +7;
Δ = b2-4ac
Δ = -72-4·(-60)·7
Δ = 1729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{1729}}{2*-60}=\frac{7-\sqrt{1729}}{-120}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{1729}}{2*-60}=\frac{7+\sqrt{1729}}{-120}
$