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x=x/6x-30
We move all terms to the left:
x-(x/6x-30)=0
Domain of the equation: 6x-30)!=0We get rid of parentheses
x∈R
x-x/6x+30=0
We multiply all the terms by the denominator
x*6x-x+30*6x=0
We add all the numbers together, and all the variables
-1x+x*6x+30*6x=0
Wy multiply elements
6x^2-1x+180x=0
We add all the numbers together, and all the variables
6x^2+179x=0
a = 6; b = 179; c = 0;
Δ = b2-4ac
Δ = 1792-4·6·0
Δ = 32041
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{32041}=179$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(179)-179}{2*6}=\frac{-358}{12} =-29+5/6 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(179)+179}{2*6}=\frac{0}{12} =0 $
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