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5+x=42/x
We move all terms to the left:
5+x-(42/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-(+42/x)+5=0
We get rid of parentheses
x-42/x+5=0
We multiply all the terms by the denominator
x*x+5*x-42=0
We add all the numbers together, and all the variables
5x+x*x-42=0
Wy multiply elements
x^2+5x-42=0
a = 1; b = 5; c = -42;
Δ = b2-4ac
Δ = 52-4·1·(-42)
Δ = 193
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{193}}{2*1}=\frac{-5-\sqrt{193}}{2}x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{193}}{2*1}=\frac{-5+\sqrt{193}}{2}
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