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x-1/5x=84
We move all terms to the left:
x-1/5x-(84)=0
Domain of the equation: 5x!=0We multiply all the terms by the denominator
x!=0/5
x!=0
x∈R
x*5x-84*5x-1=0
Wy multiply elements
5x^2-420x-1=0
a = 5; b = -420; c = -1;
Δ = b2-4ac
Δ = -4202-4·5·(-1)
Δ = 176420
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{176420}=\sqrt{4*44105}=\sqrt{4}*\sqrt{44105}=2\sqrt{44105}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-420)-2\sqrt{44105}}{2*5}=\frac{420-2\sqrt{44105}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-420)+2\sqrt{44105}}{2*5}=\frac{420+2\sqrt{44105}}{10} $
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