3(2x/2)=2/3x-46

Solution for 3(2x/2)=2/3x-46 equation:

3(2x/2)=2/3x-46

We move all terms to the left:

3(2x/2)-(2/3x-46)=0


Domain of the equation: 3x-46)!=0

x∈R


We add all the numbers together, and all the variables

3(+2x/2)-(2/3x-46)=0

We multiply parentheses

6x-(2/3x-46)=0

We get rid of parentheses

6x-2/3x+46=0

We multiply all the terms by the denominator


6x*3x+46*3x-2=0

Wy multiply elements

18x^2+138x-2=0

a = 18; b = 138; c = -2;
Δ = b2-4ac
Δ = 1382-4·18·(-2)
Δ = 19188
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:

$\sqrt{\Delta}=\sqrt{19188}=\sqrt{36*533}=\sqrt{36}*\sqrt{533}=6\sqrt{533}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(138)-6\sqrt{533}}{2*18}=\frac{-138-6\sqrt{533}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(138)+6\sqrt{533}}{2*18}=\frac{-138+6\sqrt{533}}{36}
$