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X-1/3X=4
We move all terms to the left:
X-1/3X-(4)=0
Domain of the equation: 3X!=0We multiply all the terms by the denominator
X!=0/3
X!=0
X∈R
X*3X-4*3X-1=0
Wy multiply elements
3X^2-12X-1=0
a = 3; b = -12; c = -1;
Δ = b2-4ac
Δ = -122-4·3·(-1)
Δ = 156
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{39}}{2*3}=\frac{12-2\sqrt{39}}{6} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{39}}{2*3}=\frac{12+2\sqrt{39}}{6} $
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