2/3x-3=x+18

Solution for 2/3x-3=x+18 equation:

2/3x-3=x+18

We move all terms to the left:

2/3x-3-(x+18)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

2/3x-x-18-3=0

We multiply all the terms by the denominator


-x*3x-18*3x-3*3x+2=0

Wy multiply elements

-3x^2-54x-9x+2=0

We add all the numbers together, and all the variables

-3x^2-63x+2=0

a = -3; b = -63; c = +2;
Δ = b2-4ac
Δ = -632-4·(-3)·2
Δ = 3993
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:

$\sqrt{\Delta}=\sqrt{3993}=\sqrt{121*33}=\sqrt{121}*\sqrt{33}=11\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-63)-11\sqrt{33}}{2*-3}=\frac{63-11\sqrt{33}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+11\sqrt{33}}{2*-3}=\frac{63+11\sqrt{33}}{-6}
$