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1x+1/4x=210
We move all terms to the left:
1x+1/4x-(210)=0
Domain of the equation: 4x!=0We add all the numbers together, and all the variables
x!=0/4
x!=0
x∈R
x+1/4x-210=0
We multiply all the terms by the denominator
x*4x-210*4x+1=0
Wy multiply elements
4x^2-840x+1=0
a = 4; b = -840; c = +1;
Δ = b2-4ac
Δ = -8402-4·4·1
Δ = 705584
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{705584}=\sqrt{16*44099}=\sqrt{16}*\sqrt{44099}=4\sqrt{44099}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-840)-4\sqrt{44099}}{2*4}=\frac{840-4\sqrt{44099}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-840)+4\sqrt{44099}}{2*4}=\frac{840+4\sqrt{44099}}{8} $
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