2/3x-2=4x+18

Solution for 2/3x-2=4x+18 equation:

2/3x-2=4x+18

We move all terms to the left:

2/3x-2-(4x+18)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

2/3x-4x-18-2=0

We multiply all the terms by the denominator


-4x*3x-18*3x-2*3x+2=0

Wy multiply elements

-12x^2-54x-6x+2=0

We add all the numbers together, and all the variables

-12x^2-60x+2=0

a = -12; b = -60; c = +2;
Δ = b2-4ac
Δ = -602-4·(-12)·2
Δ = 3696
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:

$\sqrt{\Delta}=\sqrt{3696}=\sqrt{16*231}=\sqrt{16}*\sqrt{231}=4\sqrt{231}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-4\sqrt{231}}{2*-12}=\frac{60-4\sqrt{231}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+4\sqrt{231}}{2*-12}=\frac{60+4\sqrt{231}}{-24}
$