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1/x+x-90=0
Domain of the equation: x!=0We add all the numbers together, and all the variables
x∈R
x+1/x-90=0
We multiply all the terms by the denominator
x*x-90*x+1=0
We add all the numbers together, and all the variables
-90x+x*x+1=0
Wy multiply elements
x^2-90x+1=0
a = 1; b = -90; c = +1;
Δ = b2-4ac
Δ = -902-4·1·1
Δ = 8096
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{8096}=\sqrt{16*506}=\sqrt{16}*\sqrt{506}=4\sqrt{506}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-4\sqrt{506}}{2*1}=\frac{90-4\sqrt{506}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+4\sqrt{506}}{2*1}=\frac{90+4\sqrt{506}}{2} $
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