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x+2/3x=158
We move all terms to the left:
x+2/3x-(158)=0
Domain of the equation: 3x!=0We multiply all the terms by the denominator
x!=0/3
x!=0
x∈R
x*3x-158*3x+2=0
Wy multiply elements
3x^2-474x+2=0
a = 3; b = -474; c = +2;
Δ = b2-4ac
Δ = -4742-4·3·2
Δ = 224652
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{224652}=\sqrt{4*56163}=\sqrt{4}*\sqrt{56163}=2\sqrt{56163}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-474)-2\sqrt{56163}}{2*3}=\frac{474-2\sqrt{56163}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-474)+2\sqrt{56163}}{2*3}=\frac{474+2\sqrt{56163}}{6} $
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