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x+16=20/x=4
We move all terms to the left:
x+16-(20/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-(+20/x)+16=0
We get rid of parentheses
x-20/x+16=0
We multiply all the terms by the denominator
x*x+16*x-20=0
We add all the numbers together, and all the variables
16x+x*x-20=0
Wy multiply elements
x^2+16x-20=0
a = 1; b = 16; c = -20;
Δ = b2-4ac
Δ = 162-4·1·(-20)
Δ = 336
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{21}}{2*1}=\frac{-16-4\sqrt{21}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{21}}{2*1}=\frac{-16+4\sqrt{21}}{2} $
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