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5x+2/3x=102
We move all terms to the left:
5x+2/3x-(102)=0
Domain of the equation: 3x!=0We multiply all the terms by the denominator
x!=0/3
x!=0
x∈R
5x*3x-102*3x+2=0
Wy multiply elements
15x^2-306x+2=0
a = 15; b = -306; c = +2;
Δ = b2-4ac
Δ = -3062-4·15·2
Δ = 93516
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{93516}=\sqrt{4*23379}=\sqrt{4}*\sqrt{23379}=2\sqrt{23379}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-306)-2\sqrt{23379}}{2*15}=\frac{306-2\sqrt{23379}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-306)+2\sqrt{23379}}{2*15}=\frac{306+2\sqrt{23379}}{30} $
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