(24)(39)=(2x-4)(x-6)

Solution for (24)(39)=(2x-4)(x-6) equation:

(24)(39)=(2x-4)(x-6)

We move all terms to the left:

(24)(39)-((2x-4)(x-6))=0

We multiply parentheses ..

-((+2x^2-12x-4x+24))+2439=0


We calculate terms in parentheses: -((+2x^2-12x-4x+24)), so:

(+2x^2-12x-4x+24)

We get rid of parentheses

2x^2-12x-4x+24

We add all the numbers together, and all the variables

2x^2-16x+24

Back to the equation:

-(2x^2-16x+24)


We get rid of parentheses

-2x^2+16x-24+2439=0

We add all the numbers together, and all the variables

-2x^2+16x+2415=0

a = -2; b = 16; c = +2415;
Δ = b2-4ac
Δ = 162-4·(-2)·2415
Δ = 19576
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:

$\sqrt{\Delta}=\sqrt{19576}=\sqrt{4*4894}=\sqrt{4}*\sqrt{4894}=2\sqrt{4894}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{4894}}{2*-2}=\frac{-16-2\sqrt{4894}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{4894}}{2*-2}=\frac{-16+2\sqrt{4894}}{-4}
$