X=x(x-3)-4

Solution for X=x(x-3)-4 equation:

X=X(X-3)-4

We move all terms to the left:

X-(X(X-3)-4)=0


We calculate terms in parentheses: -(X(X-3)-4), so:

X(X-3)-4

We multiply parentheses

X^2-3X-4

Back to the equation:

-(X^2-3X-4)


We get rid of parentheses

-X^2+X+3X+4=0

We add all the numbers together, and all the variables

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

a = -1; b = 4; c = +4;
Δ = b2-4ac
Δ = 42-4·(-1)·4
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*-1}=\frac{-4-4\sqrt{2}}{-2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{2}}{2*-1}=\frac{-4+4\sqrt{2}}{-2}
$