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5/6x-1/9x=102
We move all terms to the left:
5/6x-1/9x-(102)=0
Domain of the equation: 6x!=0
x!=0/6
x!=0
x∈R
Domain of the equation: 9x!=0We calculate fractions
x!=0/9
x!=0
x∈R
45x/54x^2+(-6x)/54x^2-102=0
We multiply all the terms by the denominator
45x+(-6x)-102*54x^2=0
Wy multiply elements
-5508x^2+45x+(-6x)=0
We get rid of parentheses
-5508x^2+45x-6x=0
We add all the numbers together, and all the variables
-5508x^2+39x=0
a = -5508; b = 39; c = 0;
Δ = b2-4ac
Δ = 392-4·(-5508)·0
Δ = 1521
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{1521}=39$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(39)-39}{2*-5508}=\frac{-78}{-11016} =13/1836 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+39}{2*-5508}=\frac{0}{-11016} =0 $
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