18+x=1/5x

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}
$