-x-2=2/5x+1

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

-x-2=2/5x+1

We move all terms to the left:

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


Domain of the equation: 5x+1)!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

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

a = -5; b = -15; c = -2;
Δ = b2-4ac
Δ = -152-4·(-5)·(-2)
Δ = 185
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{-(-15)-\sqrt{185}}{2*-5}=\frac{15-\sqrt{185}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{185}}{2*-5}=\frac{15+\sqrt{185}}{-10}
$