5x=x+5/3x+7

Solution for 5x=x+5/3x+7 equation:

5x=x+5/3x+7

We move all terms to the left:

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


Domain of the equation: 3x+7)!=0

x∈R


We get rid of parentheses

5x-x-5/3x-7=0

We multiply all the terms by the denominator


5x*3x-x*3x-7*3x-5=0

Wy multiply elements

15x^2-3x^2-21x-5=0

We add all the numbers together, and all the variables

12x^2-21x-5=0

a = 12; b = -21; c = -5;
Δ = b2-4ac
Δ = -212-4·12·(-5)
Δ = 681
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{-(-21)-\sqrt{681}}{2*12}=\frac{21-\sqrt{681}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{681}}{2*12}=\frac{21+\sqrt{681}}{24}
$