X-3=5/3x+8

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

X-3=5/3X+8

We move all terms to the left:

X-3-(5/3X+8)=0


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

X∈R


We get rid of parentheses

X-5/3X-8-3=0

We multiply all the terms by the denominator


X*3X-8*3X-3*3X-5=0

Wy multiply elements

3X^2-24X-9X-5=0

We add all the numbers together, and all the variables

3X^2-33X-5=0

a = 3; b = -33; c = -5;
Δ = b2-4ac
Δ = -332-4·3·(-5)
Δ = 1149
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{1149}}{2*3}=\frac{33-\sqrt{1149}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+\sqrt{1149}}{2*3}=\frac{33+\sqrt{1149}}{6}
$