(12/3x)x=62/3

Solution for (12/3x)x=62/3 equation:

(12/3x)x=62/3

We move all terms to the left:

(12/3x)x-(62/3)=0


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

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+12/3x)x-(+62/3)=0

We multiply parentheses

12x^2-(+62/3)=0

We get rid of parentheses

12x^2-62/3=0

We multiply all the terms by the denominator


12x^2*3-62=0

Wy multiply elements

36x^2-62=0

a = 36; b = 0; c = -62;
Δ = b2-4ac
Δ = 02-4·36·(-62)
Δ = 8928
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:

$\sqrt{\Delta}=\sqrt{8928}=\sqrt{144*62}=\sqrt{144}*\sqrt{62}=12\sqrt{62}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{62}}{2*36}=\frac{0-12\sqrt{62}}{72}
=-\frac{12\sqrt{62}}{72}
=-\frac{\sqrt{62}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{62}}{2*36}=\frac{0+12\sqrt{62}}{72}
=\frac{12\sqrt{62}}{72}
=\frac{\sqrt{62}}{6}
$