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3x-2/5x=39
We move all terms to the left:
3x-2/5x-(39)=0
Domain of the equation: 5x!=0We multiply all the terms by the denominator
x!=0/5
x!=0
x∈R
3x*5x-39*5x-2=0
Wy multiply elements
15x^2-195x-2=0
a = 15; b = -195; c = -2;
Δ = b2-4ac
Δ = -1952-4·15·(-2)
Δ = 38145
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{-(-195)-\sqrt{38145}}{2*15}=\frac{195-\sqrt{38145}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-195)+\sqrt{38145}}{2*15}=\frac{195+\sqrt{38145}}{30} $
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