1/5x+18=x

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

1/5x+18=x

We move all terms to the left:

1/5x+18-(x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+1/5x+18=0

We multiply all the terms by the denominator


-1x*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}
$