6x-14=7/3x

Solution for 6x-14=7/3x equation:

6x-14=7/3x

We move all terms to the left:

6x-14-(7/3x)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

6x-(+7/3x)-14=0

We get rid of parentheses

6x-7/3x-14=0

We multiply all the terms by the denominator


6x*3x-14*3x-7=0

Wy multiply elements

18x^2-42x-7=0

a = 18; b = -42; c = -7;
Δ = b2-4ac
Δ = -422-4·18·(-7)
Δ = 2268
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:

$\sqrt{\Delta}=\sqrt{2268}=\sqrt{324*7}=\sqrt{324}*\sqrt{7}=18\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-18\sqrt{7}}{2*18}=\frac{42-18\sqrt{7}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+18\sqrt{7}}{2*18}=\frac{42+18\sqrt{7}}{36}
$