-1+(5/6)(-6x-3)-x=-x

Solution for -1+(5/6)(-6x-3)-x=-x equation:

-1+(5/6)(-6x-3)-x=-x

We move all terms to the left:

-1+(5/6)(-6x-3)-x-(-x)=0


Domain of the equation: 6)(-6x-3)!=0

x∈R


We add all the numbers together, and all the variables

(+5/6)(-6x-3)-x-(-1x)-1=0

We add all the numbers together, and all the variables

-1x+(+5/6)(-6x-3)-(-1x)-1=0

We get rid of parentheses

-1x+(+5/6)(-6x-3)+1x-1=0

We multiply parentheses ..

(-30x^2+5/6*-3)-1x+1x-1=0

We multiply all the terms by the denominator


(-30x^2+5-1x*6*-3)+1x*6*-3)-1*6*-3)=0

We add all the numbers together, and all the variables

(-30x^2+5-1x*6*-3)+1x*6*=0

Wy multiply elements

(-30x^2+5-1x*6*-3)+6x^2=0

We get rid of parentheses

-30x^2+6x^2-1x*6*+5-3=0

We add all the numbers together, and all the variables

-24x^2-1x*6*+2=0

Wy multiply elements

-24x^2-6x^2+2=0

We add all the numbers together, and all the variables

-30x^2+2=0

a = -30; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-30)·2
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{15}}{2*-30}=\frac{0-4\sqrt{15}}{-60}
=-\frac{4\sqrt{15}}{-60}
=-\frac{\sqrt{15}}{-15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{15}}{2*-30}=\frac{0+4\sqrt{15}}{-60}
=\frac{4\sqrt{15}}{-60}
=\frac{\sqrt{15}}{-15}
$