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

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

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

We move all terms to the left:

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

We multiply parentheses

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


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

3x(x+2)-3

We multiply parentheses

3x^2+6x-3

Back to the equation:

-(3x^2+6x-3)


We get rid of parentheses

x^2-3x^2-2x-6x+3=0

We add all the numbers together, and all the variables

-2x^2-8x+3=0

a = -2; b = -8; c = +3;
Δ = b2-4ac
Δ = -82-4·(-2)·3
Δ = 88
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:

$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{22}}{2*-2}=\frac{8-2\sqrt{22}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{22}}{2*-2}=\frac{8+2\sqrt{22}}{-4}
$