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12/2x=3x
We move all terms to the left:
12/2x-(3x)=0
Domain of the equation: 2x!=0We add all the numbers together, and all the variables
x!=0/2
x!=0
x∈R
-3x+12/2x=0
We multiply all the terms by the denominator
-3x*2x+12=0
Wy multiply elements
-6x^2+12=0
a = -6; b = 0; c = +12;
Δ = b2-4ac
Δ = 02-4·(-6)·12
Δ = 288
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{2}}{2*-6}=\frac{0-12\sqrt{2}}{-12} =-\frac{12\sqrt{2}}{-12} =-\frac{\sqrt{2}}{-1} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{2}}{2*-6}=\frac{0+12\sqrt{2}}{-12} =\frac{12\sqrt{2}}{-12} =\frac{\sqrt{2}}{-1} $
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