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8/3x+1/3x=4x
We move all terms to the left:
8/3x+1/3x-(4x)=0
Domain of the equation: 3x!=0We add all the numbers together, and all the variables
x!=0/3
x!=0
x∈R
-4x+8/3x+1/3x=0
We multiply all the terms by the denominator
-4x*3x+8+1=0
We add all the numbers together, and all the variables
-4x*3x+9=0
Wy multiply elements
-12x^2+9=0
a = -12; b = 0; c = +9;
Δ = b2-4ac
Δ = 02-4·(-12)·9
Δ = 432
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{3}}{2*-12}=\frac{0-12\sqrt{3}}{-24} =-\frac{12\sqrt{3}}{-24} =-\frac{\sqrt{3}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{3}}{2*-12}=\frac{0+12\sqrt{3}}{-24} =\frac{12\sqrt{3}}{-24} =\frac{\sqrt{3}}{-2} $
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