x+8=1/3x-3

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

x+8=1/3x-3

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

x-1/3x+3+8=0

We multiply all the terms by the denominator


x*3x+3*3x+8*3x-1=0

Wy multiply elements

3x^2+9x+24x-1=0

We add all the numbers together, and all the variables

3x^2+33x-1=0

a = 3; b = 33; c = -1;
Δ = b2-4ac
Δ = 332-4·3·(-1)
Δ = 1101
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{-(33)-\sqrt{1101}}{2*3}=\frac{-33-\sqrt{1101}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+\sqrt{1101}}{2*3}=\frac{-33+\sqrt{1101}}{6}
$