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

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

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

We move all terms to the left:

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


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

x∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

3x-(1/3x-1)+15=0

We get rid of parentheses

3x-1/3x+1+15=0

We multiply all the terms by the denominator


3x*3x+1*3x+15*3x-1=0

Wy multiply elements

9x^2+3x+45x-1=0

We add all the numbers together, and all the variables

9x^2+48x-1=0

a = 9; b = 48; c = -1;
Δ = b2-4ac
Δ = 482-4·9·(-1)
Δ = 2340
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:

$\sqrt{\Delta}=\sqrt{2340}=\sqrt{36*65}=\sqrt{36}*\sqrt{65}=6\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-6\sqrt{65}}{2*9}=\frac{-48-6\sqrt{65}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+6\sqrt{65}}{2*9}=\frac{-48+6\sqrt{65}}{18}
$