18=x-1/5x

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Solution for 18=x-1/5x equation:



18=x-1/5x
We move all terms to the left:
18-(x-1/5x)=0
Domain of the equation: 5x)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
-(+x-1/5x)+18=0
We get rid of parentheses
-x+1/5x+18=0
We multiply all the terms by the denominator
-x*5x+18*5x+1=0
Wy multiply elements
-5x^2+90x+1=0
a = -5; b = 90; c = +1;
Δ = b2-4ac
Δ = 902-4·(-5)·1
Δ = 8120
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:
$\sqrt{\Delta}=\sqrt{8120}=\sqrt{4*2030}=\sqrt{4}*\sqrt{2030}=2\sqrt{2030}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-2\sqrt{2030}}{2*-5}=\frac{-90-2\sqrt{2030}}{-10} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+2\sqrt{2030}}{2*-5}=\frac{-90+2\sqrt{2030}}{-10} $

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