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3x+1/3x=88
We move all terms to the left:
3x+1/3x-(88)=0
Domain of the equation: 3x!=0We multiply all the terms by the denominator
x!=0/3
x!=0
x∈R
3x*3x-88*3x+1=0
Wy multiply elements
9x^2-264x+1=0
a = 9; b = -264; c = +1;
Δ = b2-4ac
Δ = -2642-4·9·1
Δ = 69660
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{69660}=\sqrt{324*215}=\sqrt{324}*\sqrt{215}=18\sqrt{215}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-264)-18\sqrt{215}}{2*9}=\frac{264-18\sqrt{215}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-264)+18\sqrt{215}}{2*9}=\frac{264+18\sqrt{215}}{18} $
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