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x/2x+18-6x=-2
We move all terms to the left:
x/2x+18-6x-(-2)=0
Domain of the equation: 2x!=0We add all the numbers together, and all the variables
x!=0/2
x!=0
x∈R
-6x+x/2x+20=0
We multiply all the terms by the denominator
-6x*2x+x+20*2x=0
We add all the numbers together, and all the variables
x-6x*2x+20*2x=0
Wy multiply elements
-12x^2+x+40x=0
We add all the numbers together, and all the variables
-12x^2+41x=0
a = -12; b = 41; c = 0;
Δ = b2-4ac
Δ = 412-4·(-12)·0
Δ = 1681
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{1681}=41$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(41)-41}{2*-12}=\frac{-82}{-24} =3+5/12 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41)+41}{2*-12}=\frac{0}{-24} =0 $
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