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6x-13=50/x
We move all terms to the left:
6x-13-(50/x)=0
Domain of the equation: x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
6x-(+50/x)-13=0
We get rid of parentheses
6x-50/x-13=0
We multiply all the terms by the denominator
6x*x-13*x-50=0
We add all the numbers together, and all the variables
-13x+6x*x-50=0
Wy multiply elements
6x^2-13x-50=0
a = 6; b = -13; c = -50;
Δ = b2-4ac
Δ = -132-4·6·(-50)
Δ = 1369
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{1369}=37$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-37}{2*6}=\frac{-24}{12} =-2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+37}{2*6}=\frac{50}{12} =4+1/6 $
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