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2x-9/3x-2=4
We move all terms to the left:
2x-9/3x-2-(4)=0
Domain of the equation: 3x!=0We add all the numbers together, and all the variables
x!=0/3
x!=0
x∈R
2x-9/3x-6=0
We multiply all the terms by the denominator
2x*3x-6*3x-9=0
Wy multiply elements
6x^2-18x-9=0
a = 6; b = -18; c = -9;
Δ = b2-4ac
Δ = -182-4·6·(-9)
Δ = 540
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{540}=\sqrt{36*15}=\sqrt{36}*\sqrt{15}=6\sqrt{15}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{15}}{2*6}=\frac{18-6\sqrt{15}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{15}}{2*6}=\frac{18+6\sqrt{15}}{12} $
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