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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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


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

-x(x-3)

We multiply parentheses

-x^2+3x

We add all the numbers together, and all the variables

-1x^2+3x

Back to the equation:

-(-1x^2+3x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

2x^2-4x-2=0

a = 2; b = -4; c = -2;
Δ = b2-4ac
Δ = -42-4·2·(-2)
Δ = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{2}}{2*2}=\frac{4-4\sqrt{2}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{2}}{2*2}=\frac{4+4\sqrt{2}}{4}
$