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3x+2=2/3x+4.333
We move all terms to the left:
3x+2-(2/3x+4.333)=0
Domain of the equation: 3x+4.333)!=0We get rid of parentheses
x∈R
3x-2/3x-4.333+2=0
We multiply all the terms by the denominator
3x*3x-(4.333)*3x+2*3x-2=0
We multiply parentheses
3x*3x-12.999x+2*3x-2=0
Wy multiply elements
9x^2-12.999x+6x-2=0
We add all the numbers together, and all the variables
9x^2-6.999x-2=0
a = 9; b = -6.999; c = -2;
Δ = b2-4ac
Δ = -6.9992-4·9·(-2)
Δ = 120.986001
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{-(-6.999)-\sqrt{120.986001}}{2*9}=\frac{6.999-\sqrt{120.986001}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6.999)+\sqrt{120.986001}}{2*9}=\frac{6.999+\sqrt{120.986001}}{18} $
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