12x2/3=83-1/3

Solution for 12x2/3=83-1/3 equation:

12x^2/3=83-1/3

We move all terms to the left:

12x^2/3-(83-1/3)=0

We add all the numbers together, and all the variables

12x^2/3-(-1/3+83)=0

We get rid of parentheses

12x^2/3-83+1/3=0

We multiply all the terms by the denominator


12x^2+1-83*3=0

We add all the numbers together, and all the variables

12x^2-248=0

a = 12; b = 0; c = -248;
Δ = b2-4ac
Δ = 02-4·12·(-248)
Δ = 11904
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:

$\sqrt{\Delta}=\sqrt{11904}=\sqrt{64*186}=\sqrt{64}*\sqrt{186}=8\sqrt{186}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{186}}{2*12}=\frac{0-8\sqrt{186}}{24}
=-\frac{8\sqrt{186}}{24}
=-\frac{\sqrt{186}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{186}}{2*12}=\frac{0+8\sqrt{186}}{24}
=\frac{8\sqrt{186}}{24}
=\frac{\sqrt{186}}{3}
$