X+3=1/3x+8

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

X+3=1/3X+8

We move all terms to the left:

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


Domain of the equation: 3X+8)!=0

X∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

3X^2-15X-1=0

a = 3; b = -15; c = -1;
Δ = b2-4ac
Δ = -152-4·3·(-1)
Δ = 237
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{-(-15)-\sqrt{237}}{2*3}=\frac{15-\sqrt{237}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{237}}{2*3}=\frac{15+\sqrt{237}}{6}
$