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x+2/3x=97
We move all terms to the left:
x+2/3x-(97)=0
Domain of the equation: 3x!=0We multiply all the terms by the denominator
x!=0/3
x!=0
x∈R
x*3x-97*3x+2=0
Wy multiply elements
3x^2-291x+2=0
a = 3; b = -291; c = +2;
Δ = b2-4ac
Δ = -2912-4·3·2
Δ = 84657
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{-(-291)-\sqrt{84657}}{2*3}=\frac{291-\sqrt{84657}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-291)+\sqrt{84657}}{2*3}=\frac{291+\sqrt{84657}}{6} $
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