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2/3x-4x+1=0
Domain of the equation: 3x!=0We add all the numbers together, and all the variables
x!=0/3
x!=0
x∈R
-4x+2/3x+1=0
We multiply all the terms by the denominator
-4x*3x+1*3x+2=0
Wy multiply elements
-12x^2+3x+2=0
a = -12; b = 3; c = +2;
Δ = b2-4ac
Δ = 32-4·(-12)·2
Δ = 105
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{105}}{2*-12}=\frac{-3-\sqrt{105}}{-24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{105}}{2*-12}=\frac{-3+\sqrt{105}}{-24} $
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