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X-2/3X=-2
We move all terms to the left:
X-2/3X-(-2)=0
Domain of the equation: 3X!=0We add all the numbers together, and all the variables
X!=0/3
X!=0
X∈R
X-2/3X+2=0
We multiply all the terms by the denominator
X*3X+2*3X-2=0
Wy multiply elements
3X^2+6X-2=0
a = 3; b = 6; c = -2;
Δ = b2-4ac
Δ = 62-4·3·(-2)
Δ = 60
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{15}}{2*3}=\frac{-6-2\sqrt{15}}{6} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{15}}{2*3}=\frac{-6+2\sqrt{15}}{6} $
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