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5x+7/3x-1=6
We move all terms to the left:
5x+7/3x-1-(6)=0
Domain of the equation: 3x!=0We add all the numbers together, and all the variables
x!=0/3
x!=0
x∈R
5x+7/3x-7=0
We multiply all the terms by the denominator
5x*3x-7*3x+7=0
Wy multiply elements
15x^2-21x+7=0
a = 15; b = -21; c = +7;
Δ = b2-4ac
Δ = -212-4·15·7
Δ = 21
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{21}}{2*15}=\frac{21-\sqrt{21}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{21}}{2*15}=\frac{21+\sqrt{21}}{30} $
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