(x+3)(x-1)=2(x*x-9)

Solution for (x+3)(x-1)=2(x*x-9) equation:

(x+3)(x-1)=2(x*x-9)

We move all terms to the left:

(x+3)(x-1)-(2(x*x-9))=0

We multiply parentheses ..

(+x^2-1x+3x-3)-(2(x*x-9))=0


We calculate terms in parentheses: -(2(x*x-9)), so:

2(x*x-9)

We multiply parentheses

2x^2-18

Back to the equation:

-(2x^2-18)


We get rid of parentheses

x^2-2x^2-1x+3x-3+18=0

We add all the numbers together, and all the variables

-1x^2+2x+15=0

a = -1; b = 2; c = +15;
Δ = b2-4ac
Δ = 22-4·(-1)·15
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-8}{2*-1}=\frac{-10}{-2}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+8}{2*-1}=\frac{6}{-2}
=-3
$