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-5/3x=9-2x
We move all terms to the left:
-5/3x-(9-2x)=0
Domain of the equation: 3x!=0We add all the numbers together, and all the variables
x!=0/3
x!=0
x∈R
-5/3x-(-2x+9)=0
We get rid of parentheses
-5/3x+2x-9=0
We multiply all the terms by the denominator
2x*3x-9*3x-5=0
Wy multiply elements
6x^2-27x-5=0
a = 6; b = -27; c = -5;
Δ = b2-4ac
Δ = -272-4·6·(-5)
Δ = 849
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{-(-27)-\sqrt{849}}{2*6}=\frac{27-\sqrt{849}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+\sqrt{849}}{2*6}=\frac{27+\sqrt{849}}{12} $
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