1/5x-0.2=x+2

Solution for 1/5x-0.2=x+2 equation:

1/5x-0.2=x+2

We move all terms to the left:

1/5x-0.2-(x+2)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

1/5x-x-2-0.2=0

We multiply all the terms by the denominator


-x*5x-2*5x-(0.2)*5x+1=0

We multiply parentheses

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

Wy multiply elements

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

We add all the numbers together, and all the variables

-5x^2-11x+1=0

a = -5; b = -11; c = +1;
Δ = b2-4ac
Δ = -112-4·(-5)·1
Δ = 141
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-\sqrt{141}}{2*-5}=\frac{11-\sqrt{141}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{141}}{2*-5}=\frac{11+\sqrt{141}}{-10}
$