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6x+5=17/x=
We move all terms to the left:
6x+5-(17/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-(+17/x)+5=0
We get rid of parentheses
6x-17/x+5=0
We multiply all the terms by the denominator
6x*x+5*x-17=0
We add all the numbers together, and all the variables
5x+6x*x-17=0
Wy multiply elements
6x^2+5x-17=0
a = 6; b = 5; c = -17;
Δ = b2-4ac
Δ = 52-4·6·(-17)
Δ = 433
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{433}}{2*6}=\frac{-5-\sqrt{433}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{433}}{2*6}=\frac{-5+\sqrt{433}}{12} $
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