-2/5x-6=x

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

-2/5x-6=x

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

a = -5; b = -30; c = -2;
Δ = b2-4ac
Δ = -302-4·(-5)·(-2)
Δ = 860
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:

$\sqrt{\Delta}=\sqrt{860}=\sqrt{4*215}=\sqrt{4}*\sqrt{215}=2\sqrt{215}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{215}}{2*-5}=\frac{30-2\sqrt{215}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{215}}{2*-5}=\frac{30+2\sqrt{215}}{-10}
$