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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

6x^2-66x+2=0

a = 6; b = -66; c = +2;
Δ = b2-4ac
Δ = -662-4·6·2
Δ = 4308
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:

$\sqrt{\Delta}=\sqrt{4308}=\sqrt{4*1077}=\sqrt{4}*\sqrt{1077}=2\sqrt{1077}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-2\sqrt{1077}}{2*6}=\frac{66-2\sqrt{1077}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+2\sqrt{1077}}{2*6}=\frac{66+2\sqrt{1077}}{12}
$