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2/3x-9=5x-12
We move all terms to the left:
2/3x-9-(5x-12)=0
Domain of the equation: 3x!=0We get rid of parentheses
x!=0/3
x!=0
x∈R
2/3x-5x+12-9=0
We multiply all the terms by the denominator
-5x*3x+12*3x-9*3x+2=0
Wy multiply elements
-15x^2+36x-27x+2=0
We add all the numbers together, and all the variables
-15x^2+9x+2=0
a = -15; b = 9; c = +2;
Δ = b2-4ac
Δ = 92-4·(-15)·2
Δ = 201
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{-(9)-\sqrt{201}}{2*-15}=\frac{-9-\sqrt{201}}{-30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{201}}{2*-15}=\frac{-9+\sqrt{201}}{-30} $
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