1/5x+x=18

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

1/5x+x=18

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

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 = 8080
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:

$\sqrt{\Delta}=\sqrt{8080}=\sqrt{16*505}=\sqrt{16}*\sqrt{505}=4\sqrt{505}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-4\sqrt{505}}{2*5}=\frac{90-4\sqrt{505}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+4\sqrt{505}}{2*5}=\frac{90+4\sqrt{505}}{10}
$