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

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

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

We move all terms to the left:

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

We multiply parentheses

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


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

(x-1)2-2

We multiply parentheses

2x-2-2

We add all the numbers together, and all the variables

2x-4

Back to the equation:

-(2x-4)


We add all the numbers together, and all the variables

-1x^2-1x-(2x-4)=0

We get rid of parentheses

-1x^2-1x-2x+4=0

We add all the numbers together, and all the variables

-1x^2-3x+4=0

a = -1; b = -3; c = +4;
Δ = b2-4ac
Δ = -32-4·(-1)·4
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-5}{2*-1}=\frac{-2}{-2}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+5}{2*-1}=\frac{8}{-2}
=-4
$