1/5x+x=54

Solution for 1/5x+x=54 equation:

1/5x+x=54

We move all terms to the left:

1/5x+x-(54)=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-54=0

We multiply all the terms by the denominator


x*5x-54*5x+1=0

Wy multiply elements

5x^2-270x+1=0

a = 5; b = -270; c = +1;
Δ = b2-4ac
Δ = -2702-4·5·1
Δ = 72880
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:

$\sqrt{\Delta}=\sqrt{72880}=\sqrt{16*4555}=\sqrt{16}*\sqrt{4555}=4\sqrt{4555}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-270)-4\sqrt{4555}}{2*5}=\frac{270-4\sqrt{4555}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-270)+4\sqrt{4555}}{2*5}=\frac{270+4\sqrt{4555}}{10}
$