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7+x=84/x
We move all terms to the left:
7+x-(84/x)=0
Domain of the equation: x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
x-(+84/x)+7=0
We get rid of parentheses
x-84/x+7=0
We multiply all the terms by the denominator
x*x+7*x-84=0
We add all the numbers together, and all the variables
7x+x*x-84=0
Wy multiply elements
x^2+7x-84=0
a = 1; b = 7; c = -84;
Δ = b2-4ac
Δ = 72-4·1·(-84)
Δ = 385
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{-(7)-\sqrt{385}}{2*1}=\frac{-7-\sqrt{385}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{385}}{2*1}=\frac{-7+\sqrt{385}}{2} $
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