12x2/3=831/3

Solution for 12x2/3=831/3 equation:

12x^2/3=831/3

We move all terms to the left:

12x^2/3-(831/3)=0

We add all the numbers together, and all the variables

12x^2/3-277=0

We multiply all the terms by the denominator


12x^2-277*3=0

We add all the numbers together, and all the variables

12x^2-831=0

a = 12; b = 0; c = -831;
Δ = b2-4ac
Δ = 02-4·12·(-831)
Δ = 39888
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:

$\sqrt{\Delta}=\sqrt{39888}=\sqrt{144*277}=\sqrt{144}*\sqrt{277}=12\sqrt{277}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{277}}{2*12}=\frac{0-12\sqrt{277}}{24}
=-\frac{12\sqrt{277}}{24}
=-\frac{\sqrt{277}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{277}}{2*12}=\frac{0+12\sqrt{277}}{24}
=\frac{12\sqrt{277}}{24}
=\frac{\sqrt{277}}{2}
$