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28=1+3x^2/3
We move all terms to the left:
28-(1+3x^2/3)=0
We get rid of parentheses
-3x^2/3-1+28=0
We multiply all the terms by the denominator
-3x^2-1*3+28*3=0
We add all the numbers together, and all the variables
-3x^2+81=0
a = -3; b = 0; c = +81;
Δ = b2-4ac
Δ = 02-4·(-3)·81
Δ = 972
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{972}=\sqrt{324*3}=\sqrt{324}*\sqrt{3}=18\sqrt{3}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18\sqrt{3}}{2*-3}=\frac{0-18\sqrt{3}}{-6} =-\frac{18\sqrt{3}}{-6} =-\frac{3\sqrt{3}}{-1} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18\sqrt{3}}{2*-3}=\frac{0+18\sqrt{3}}{-6} =\frac{18\sqrt{3}}{-6} =\frac{3\sqrt{3}}{-1} $
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