5(x+1)(x-1)=2(3x-3)2-3x-1

Solution for 5(x+1)(x-1)=2(3x-3)2-3x-1 equation:

5(x+1)(x-1)=2(3x-3)2-3x-1

We move all terms to the left:

5(x+1)(x-1)-(2(3x-3)2-3x-1)=0

We use the square of the difference formula

x^2-(2(3x-3)2-3x-1)-1=0


We calculate terms in parentheses: -(2(3x-3)2-3x-1), so:

2(3x-3)2-3x-1

We add all the numbers together, and all the variables

-3x+2(3x-3)2-1

We multiply parentheses

-3x+12x-12-1

We add all the numbers together, and all the variables

9x-13

Back to the equation:

-(9x-13)


We get rid of parentheses

x^2-9x+13-1=0

We add all the numbers together, and all the variables

x^2-9x+12=0

a = 1; b = -9; c = +12;
Δ = b2-4ac
Δ = -92-4·1·12
Δ = 33
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{-(-9)-\sqrt{33}}{2*1}=\frac{9-\sqrt{33}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{33}}{2*1}=\frac{9+\sqrt{33}}{2}
$