1/5x=308+x

Solution for 1/5x=308+x equation:

1/5x=308+x

We move all terms to the left:

1/5x-(308+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

1/5x-(x+308)=0

We get rid of parentheses

1/5x-x-308=0

We multiply all the terms by the denominator


-x*5x-308*5x+1=0

Wy multiply elements

-5x^2-1540x+1=0

a = -5; b = -1540; c = +1;
Δ = b2-4ac
Δ = -15402-4·(-5)·1
Δ = 2371620
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:

$\sqrt{\Delta}=\sqrt{2371620}=\sqrt{3364*705}=\sqrt{3364}*\sqrt{705}=58\sqrt{705}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1540)-58\sqrt{705}}{2*-5}=\frac{1540-58\sqrt{705}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1540)+58\sqrt{705}}{2*-5}=\frac{1540+58\sqrt{705}}{-10}
$