24(-3+2x)=(18-x)(27-x)

Solution for 24(-3+2x)=(18-x)(27-x) equation:

24(-3+2x)=(18-x)(27-x)

We move all terms to the left:

24(-3+2x)-((18-x)(27-x))=0

We add all the numbers together, and all the variables

24(2x-3)-((-1x+18)(-1x+27))=0

We multiply parentheses

48x-((-1x+18)(-1x+27))-72=0

We multiply parentheses ..

-((+x^2-27x-18x+486))+48x-72=0


We calculate terms in parentheses: -((+x^2-27x-18x+486)), so:

(+x^2-27x-18x+486)

We get rid of parentheses

x^2-27x-18x+486

We add all the numbers together, and all the variables

x^2-45x+486

Back to the equation:

-(x^2-45x+486)


We add all the numbers together, and all the variables

48x-(x^2-45x+486)-72=0

We get rid of parentheses

-x^2+48x+45x-486-72=0

We add all the numbers together, and all the variables

-1x^2+93x-558=0

a = -1; b = 93; c = -558;
Δ = b2-4ac
Δ = 932-4·(-1)·(-558)
Δ = 6417
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:

$\sqrt{\Delta}=\sqrt{6417}=\sqrt{9*713}=\sqrt{9}*\sqrt{713}=3\sqrt{713}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(93)-3\sqrt{713}}{2*-1}=\frac{-93-3\sqrt{713}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(93)+3\sqrt{713}}{2*-1}=\frac{-93+3\sqrt{713}}{-2}
$