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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} $
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