1/3x-4=5-3x+8

Solution for 1/3x-4=5-3x+8 equation:

1/3x-4=5-3x+8

We move all terms to the left:

1/3x-4-(5-3x+8)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

1/3x-(-3x+13)-4=0

We get rid of parentheses

1/3x+3x-13-4=0

We multiply all the terms by the denominator


3x*3x-13*3x-4*3x+1=0

Wy multiply elements

9x^2-39x-12x+1=0

We add all the numbers together, and all the variables

9x^2-51x+1=0

a = 9; b = -51; c = +1;
Δ = b2-4ac
Δ = -512-4·9·1
Δ = 2565
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:

$\sqrt{\Delta}=\sqrt{2565}=\sqrt{9*285}=\sqrt{9}*\sqrt{285}=3\sqrt{285}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-51)-3\sqrt{285}}{2*9}=\frac{51-3\sqrt{285}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+3\sqrt{285}}{2*9}=\frac{51+3\sqrt{285}}{18}
$