1/5x-3=x+5

Solution for 1/5x-3=x+5 equation:

1/5x-3=x+5

We move all terms to the left:

1/5x-3-(x+5)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

1/5x-x-5-3=0

We multiply all the terms by the denominator


-x*5x-5*5x-3*5x+1=0

Wy multiply elements

-5x^2-25x-15x+1=0

We add all the numbers together, and all the variables

-5x^2-40x+1=0

a = -5; b = -40; c = +1;
Δ = b2-4ac
Δ = -402-4·(-5)·1
Δ = 1620
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:

$\sqrt{\Delta}=\sqrt{1620}=\sqrt{324*5}=\sqrt{324}*\sqrt{5}=18\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-18\sqrt{5}}{2*-5}=\frac{40-18\sqrt{5}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+18\sqrt{5}}{2*-5}=\frac{40+18\sqrt{5}}{-10}
$