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x/3x-7x+22=2
We move all terms to the left:
x/3x-7x+22-(2)=0
Domain of the equation: 3x!=0We add all the numbers together, and all the variables
x!=0/3
x!=0
x∈R
-7x+x/3x+20=0
We multiply all the terms by the denominator
-7x*3x+x+20*3x=0
We add all the numbers together, and all the variables
x-7x*3x+20*3x=0
Wy multiply elements
-21x^2+x+60x=0
We add all the numbers together, and all the variables
-21x^2+61x=0
a = -21; b = 61; c = 0;
Δ = b2-4ac
Δ = 612-4·(-21)·0
Δ = 3721
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{3721}=61$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(61)-61}{2*-21}=\frac{-122}{-42} =2+19/21 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(61)+61}{2*-21}=\frac{0}{-42} =0 $
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