X(x-9)=x+4(x-12)

Solution for X(x-9)=x+4(x-12) equation:

X(X-9)=X+4(X-12)

We move all terms to the left:

X(X-9)-(X+4(X-12))=0

We multiply parentheses

X^2-9X-(X+4(X-12))=0


We calculate terms in parentheses: -(X+4(X-12)), so:

X+4(X-12)

We multiply parentheses

X+4X-48

We add all the numbers together, and all the variables

5X-48

Back to the equation:

-(5X-48)


We get rid of parentheses

X^2-9X-5X+48=0

We add all the numbers together, and all the variables

X^2-14X+48=0

a = 1; b = -14; c = +48;
Δ = b2-4ac
Δ = -142-4·1·48
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{-(-14)-2}{2*1}=\frac{12}{2}
=6
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2}{2*1}=\frac{16}{2}
=8
$