168=4x+2/3x

Solution for 168=4x+2/3x equation:

168=4x+2/3x

We move all terms to the left:

168-(4x+2/3x)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(+4x+2/3x)+168=0

We get rid of parentheses

-4x-2/3x+168=0

We multiply all the terms by the denominator


-4x*3x+168*3x-2=0

Wy multiply elements

-12x^2+504x-2=0

a = -12; b = 504; c = -2;
Δ = b2-4ac
Δ = 5042-4·(-12)·(-2)
Δ = 253920
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:

$\sqrt{\Delta}=\sqrt{253920}=\sqrt{8464*30}=\sqrt{8464}*\sqrt{30}=92\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(504)-92\sqrt{30}}{2*-12}=\frac{-504-92\sqrt{30}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(504)+92\sqrt{30}}{2*-12}=\frac{-504+92\sqrt{30}}{-24}
$