1/5x+6=x-2

Solution for 1/5x+6=x-2 equation:

1/5x+6=x-2

We move all terms to the left:

1/5x+6-(x-2)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

1/5x-x+2+6=0

We multiply all the terms by the denominator


-x*5x+2*5x+6*5x+1=0

Wy multiply elements

-5x^2+10x+30x+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}
$