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2/3x-x=7
We move all terms to the left:
2/3x-x-(7)=0
Domain of the equation: 3x!=0We add all the numbers together, and all the variables
x!=0/3
x!=0
x∈R
-1x+2/3x-7=0
We multiply all the terms by the denominator
-1x*3x-7*3x+2=0
Wy multiply elements
-3x^2-21x+2=0
a = -3; b = -21; c = +2;
Δ = b2-4ac
Δ = -212-4·(-3)·2
Δ = 465
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{-(-21)-\sqrt{465}}{2*-3}=\frac{21-\sqrt{465}}{-6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{465}}{2*-3}=\frac{21+\sqrt{465}}{-6} $
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