-1/5x+1=x+3

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

-1/5x+1=x+3

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

-5x^2-10x-1=0

a = -5; b = -10; c = -1;
Δ = b2-4ac
Δ = -102-4·(-5)·(-1)
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-4\sqrt{5}}{2*-5}=\frac{10-4\sqrt{5}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+4\sqrt{5}}{2*-5}=\frac{10+4\sqrt{5}}{-10}
$