(x-2)2-3x=x(x+1)-4

Solution for (x-2)2-3x=x(x+1)-4 equation:

(x-2)2-3x=x(x+1)-4

We move all terms to the left:

(x-2)2-3x-(x(x+1)-4)=0

We add all the numbers together, and all the variables

-3x+(x-2)2-(x(x+1)-4)=0

We multiply parentheses

-3x+2x-(x(x+1)-4)-4=0


We calculate terms in parentheses: -(x(x+1)-4), so:

x(x+1)-4

We multiply parentheses

x^2+x-4

Back to the equation:

-(x^2+x-4)


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-1x^2-2x=0

a = -1; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·(-1)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*-1}=\frac{0}{-2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*-1}=\frac{4}{-2}
=-2
$