X(x-3)=-x+24

Solution for X(x-3)=-x+24 equation:

X(X-3)=-X+24

We move all terms to the left:

X(X-3)-(-X+24)=0

We add all the numbers together, and all the variables

X(X-3)-(-1X+24)=0

We multiply parentheses

X^2-3X-(-1X+24)=0

We get rid of parentheses

X^2-3X+1X-24=0

We add all the numbers together, and all the variables

X^2-2X-24=0

a = 1; b = -2; c = -24;
Δ = b2-4ac
Δ = -22-4·1·(-24)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-10}{2*1}=\frac{-8}{2}
=-4
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+10}{2*1}=\frac{12}{2}
=6
$