5=x+5/3x-1

Solution for 5=x+5/3x-1 equation:

5=x+5/3x-1

We move all terms to the left:

5-(x+5/3x-1)=0


Domain of the equation: 3x-1)!=0

x∈R


We get rid of parentheses

-x-5/3x+1+5=0

We multiply all the terms by the denominator


-x*3x+1*3x+5*3x-5=0

Wy multiply elements

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

We add all the numbers together, and all the variables

-3x^2+18x-5=0

a = -3; b = 18; c = -5;
Δ = b2-4ac
Δ = 182-4·(-3)·(-5)
Δ = 264
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{264}=\sqrt{4*66}=\sqrt{4}*\sqrt{66}=2\sqrt{66}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{66}}{2*-3}=\frac{-18-2\sqrt{66}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{66}}{2*-3}=\frac{-18+2\sqrt{66}}{-6}
$