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6x-(15/x)=13
We move all terms to the left:
6x-(15/x)-(13)=0
Domain of the equation: x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
6x-(+15/x)-13=0
We get rid of parentheses
6x-15/x-13=0
We multiply all the terms by the denominator
6x*x-13*x-15=0
We add all the numbers together, and all the variables
-13x+6x*x-15=0
Wy multiply elements
6x^2-13x-15=0
a = 6; b = -13; c = -15;
Δ = b2-4ac
Δ = -132-4·6·(-15)
Δ = 529
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{529}=23$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-23}{2*6}=\frac{-10}{12} =-5/6 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+23}{2*6}=\frac{36}{12} =3 $
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