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5x=x+5/3x+7

We move all terms to the left:

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

Domain of the equation: 3x+7)!=0We get rid of parentheses

x∈R

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 = b^{2}-4ac

Δ = -21^{2}-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} $

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