(24)(42)=(2x-6)(x+6)

Solution for (24)(42)=(2x-6)(x+6) equation:

(24)(42)=(2x-6)(x+6)

We move all terms to the left:

(24)(42)-((2x-6)(x+6))=0

We multiply parentheses ..

-((+2x^2+12x-6x-36))+2442=0


We calculate terms in parentheses: -((+2x^2+12x-6x-36)), so:

(+2x^2+12x-6x-36)

We get rid of parentheses

2x^2+12x-6x-36

We add all the numbers together, and all the variables

2x^2+6x-36

Back to the equation:

-(2x^2+6x-36)


We get rid of parentheses

-2x^2-6x+36+2442=0

We add all the numbers together, and all the variables

-2x^2-6x+2478=0

a = -2; b = -6; c = +2478;
Δ = b2-4ac
Δ = -62-4·(-2)·2478
Δ = 19860
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:

$\sqrt{\Delta}=\sqrt{19860}=\sqrt{4*4965}=\sqrt{4}*\sqrt{4965}=2\sqrt{4965}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{4965}}{2*-2}=\frac{6-2\sqrt{4965}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{4965}}{2*-2}=\frac{6+2\sqrt{4965}}{-4}
$