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x/9x+22=3x
We move all terms to the left:
x/9x+22-(3x)=0
Domain of the equation: 9x!=0We add all the numbers together, and all the variables
x!=0/9
x!=0
x∈R
-3x+x/9x+22=0
We multiply all the terms by the denominator
-3x*9x+x+22*9x=0
We add all the numbers together, and all the variables
x-3x*9x+22*9x=0
Wy multiply elements
-27x^2+x+198x=0
We add all the numbers together, and all the variables
-27x^2+199x=0
a = -27; b = 199; c = 0;
Δ = b2-4ac
Δ = 1992-4·(-27)·0
Δ = 39601
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{39601}=199$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(199)-199}{2*-27}=\frac{-398}{-54} =7+10/27 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(199)+199}{2*-27}=\frac{0}{-54} =0 $
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