x+5/3x-5=2

Solution for x+5/3x-5=2 equation:

x+5/3x-5=2

We move all terms to the left:

x+5/3x-5-(2)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

x+5/3x-7=0

We multiply all the terms by the denominator


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

Wy multiply elements

3x^2-21x+5=0

a = 3; b = -21; c = +5;
Δ = b2-4ac
Δ = -212-4·3·5
Δ = 381
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{381}}{2*3}=\frac{21-\sqrt{381}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{381}}{2*3}=\frac{21+\sqrt{381}}{6}
$