3x-(2/3x)=14

Solution for 3x-(2/3x)=14 equation:

3x-(2/3x)=14

We move all terms to the left:

3x-(2/3x)-(14)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3x-(+2/3x)-14=0

We get rid of parentheses

3x-2/3x-14=0

We multiply all the terms by the denominator


3x*3x-14*3x-2=0

Wy multiply elements

9x^2-42x-2=0

a = 9; b = -42; c = -2;
Δ = b2-4ac
Δ = -422-4·9·(-2)
Δ = 1836
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:

$\sqrt{\Delta}=\sqrt{1836}=\sqrt{36*51}=\sqrt{36}*\sqrt{51}=6\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-6\sqrt{51}}{2*9}=\frac{42-6\sqrt{51}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+6\sqrt{51}}{2*9}=\frac{42+6\sqrt{51}}{18}
$