12x2/3=83

Solution for 12x2/3=83 equation:

12x^2/3=83

We move all terms to the left:

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

We multiply all the terms by the denominator


12x^2-83*3=0

We add all the numbers together, and all the variables

12x^2-249=0

a = 12; b = 0; c = -249;
Δ = b2-4ac
Δ = 02-4·12·(-249)
Δ = 11952
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:

$\sqrt{\Delta}=\sqrt{11952}=\sqrt{144*83}=\sqrt{144}*\sqrt{83}=12\sqrt{83}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{83}}{2*12}=\frac{0-12\sqrt{83}}{24}
=-\frac{12\sqrt{83}}{24}
=-\frac{\sqrt{83}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{83}}{2*12}=\frac{0+12\sqrt{83}}{24}
=\frac{12\sqrt{83}}{24}
=\frac{\sqrt{83}}{2}
$