7/2x+1/3x=12+5/3x

Solution for 7/2x+1/3x=12+5/3x equation:

7/2x+1/3x=12+5/3x

We move all terms to the left:

7/2x+1/3x-(12+5/3x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

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

7/2x+1/3x-(5/3x+12)=0

We get rid of parentheses

7/2x+1/3x-5/3x-12=0

We calculate fractions


21x/6x^2+(-10x+1)/6x^2-12=0

We multiply all the terms by the denominator


21x+(-10x+1)-12*6x^2=0

Wy multiply elements

-72x^2+21x+(-10x+1)=0

We get rid of parentheses

-72x^2+21x-10x+1=0

We add all the numbers together, and all the variables

-72x^2+11x+1=0

a = -72; b = 11; c = +1;
Δ = b2-4ac
Δ = 112-4·(-72)·1
Δ = 409
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{-(11)-\sqrt{409}}{2*-72}=\frac{-11-\sqrt{409}}{-144}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{409}}{2*-72}=\frac{-11+\sqrt{409}}{-144}
$