(9x-24)=(x+9)(6x-5)

Solution for (9x-24)=(x+9)(6x-5) equation:

(9x-24)=(x+9)(6x-5)

We move all terms to the left:

(9x-24)-((x+9)(6x-5))=0

We get rid of parentheses

9x-((x+9)(6x-5))-24=0

We multiply parentheses ..

-((+6x^2-5x+54x-45))+9x-24=0


We calculate terms in parentheses: -((+6x^2-5x+54x-45)), so:

(+6x^2-5x+54x-45)

We get rid of parentheses

6x^2-5x+54x-45

We add all the numbers together, and all the variables

6x^2+49x-45

Back to the equation:

-(6x^2+49x-45)


We add all the numbers together, and all the variables

9x-(6x^2+49x-45)-24=0

We get rid of parentheses

-6x^2+9x-49x+45-24=0

We add all the numbers together, and all the variables

-6x^2-40x+21=0

a = -6; b = -40; c = +21;
Δ = b2-4ac
Δ = -402-4·(-6)·21
Δ = 2104
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:

$\sqrt{\Delta}=\sqrt{2104}=\sqrt{4*526}=\sqrt{4}*\sqrt{526}=2\sqrt{526}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-2\sqrt{526}}{2*-6}=\frac{40-2\sqrt{526}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+2\sqrt{526}}{2*-6}=\frac{40+2\sqrt{526}}{-12}
$