(X-6)(9x+3)=-24(x-6)

Solution for (X-6)(9x+3)=-24(x-6) equation:

(X-6)(9X+3)=-24(X-6)

We move all terms to the left:

(X-6)(9X+3)-(-24(X-6))=0

We multiply parentheses ..

(+9X^2+3X-54X-18)-(-24(X-6))=0


We calculate terms in parentheses: -(-24(X-6)), so:

-24(X-6)

We multiply parentheses

-24X+144

Back to the equation:

-(-24X+144)


We get rid of parentheses

9X^2+3X-54X+24X-18-144=0

We add all the numbers together, and all the variables

9X^2-27X-162=0

a = 9; b = -27; c = -162;
Δ = b2-4ac
Δ = -272-4·9·(-162)
Δ = 6561
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6561}=81$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-81}{2*9}=\frac{-54}{18}
=-3
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+81}{2*9}=\frac{108}{18}
=6
$