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5-x=4/x
We move all terms to the left:
5-x-(4/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-(+4/x)+5=0
We add all the numbers together, and all the variables
-1x-(+4/x)+5=0
We get rid of parentheses
-1x-4/x+5=0
We multiply all the terms by the denominator
-1x*x+5*x-4=0
We add all the numbers together, and all the variables
5x-1x*x-4=0
Wy multiply elements
-1x^2+5x-4=0
a = -1; b = 5; c = -4;
Δ = b2-4ac
Δ = 52-4·(-1)·(-4)
Δ = 9
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{9}=3$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-3}{2*-1}=\frac{-8}{-2} =+4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+3}{2*-1}=\frac{-2}{-2} =1 $
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