-2/5x-6=x+1

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

-2/5x-6=x+1

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-5x^2-5x-30x-2=0

We add all the numbers together, and all the variables

-5x^2-35x-2=0

a = -5; b = -35; c = -2;
Δ = b2-4ac
Δ = -352-4·(-5)·(-2)
Δ = 1185
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{-(-35)-\sqrt{1185}}{2*-5}=\frac{35-\sqrt{1185}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+\sqrt{1185}}{2*-5}=\frac{35+\sqrt{1185}}{-10}
$