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1.5/6x-2=-1/x+1
We move all terms to the left:
1.5/6x-2-(-1/x+1)=0
Domain of the equation: 6x!=0
x!=0/6
x!=0
x∈R
Domain of the equation: x+1)!=0We get rid of parentheses
x∈R
1.5/6x+1/x-1-2=0
We calculate fractions
(1.5x)/6x^2+6x/6x^2-1-2=0
We add all the numbers together, and all the variables
(+1.5x)/6x^2+6x/6x^2-1-2=0
We add all the numbers together, and all the variables
(+1.5x)/6x^2+6x/6x^2-3=0
We multiply all the terms by the denominator
(+1.5x)+6x-3*6x^2=0
We add all the numbers together, and all the variables
6x+(+1.5x)-3*6x^2=0
Wy multiply elements
-18x^2+6x+(+1.5x)=0
We get rid of parentheses
-18x^2+6x+1.5x=0
We add all the numbers together, and all the variables
-18x^2+7.5x=0
a = -18; b = 7.5; c = 0;
Δ = b2-4ac
Δ = 7.52-4·(-18)·0
Δ = 56.25
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7.5)-\sqrt{56.25}}{2*-18}=\frac{-7.5-\sqrt{56.25}}{-36} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7.5)+\sqrt{56.25}}{2*-18}=\frac{-7.5+\sqrt{56.25}}{-36} $
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