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