5x=x+5/3x+7

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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} $

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