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

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

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

We move all terms to the left:

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

We get rid of parentheses

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


We calculate terms in parentheses: -(6x(x-3)), so:

6x(x-3)

We multiply parentheses

6x^2-18x

Back to the equation:

-(6x^2-18x)


We add all the numbers together, and all the variables

-(6x^2-18x)+2=0

We get rid of parentheses

-6x^2+18x+2=0

a = -6; b = 18; c = +2;
Δ = b2-4ac
Δ = 182-4·(-6)·2
Δ = 372
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:

$\sqrt{\Delta}=\sqrt{372}=\sqrt{4*93}=\sqrt{4}*\sqrt{93}=2\sqrt{93}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{93}}{2*-6}=\frac{-18-2\sqrt{93}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{93}}{2*-6}=\frac{-18+2\sqrt{93}}{-12}
$