(20)(39)=(2x-6)(x+18)

Solution for (20)(39)=(2x-6)(x+18) equation:

(20)(39)=(2x-6)(x+18)

We move all terms to the left:

(20)(39)-((2x-6)(x+18))=0

We multiply parentheses ..

-((+2x^2+36x-6x-108))+2039=0


We calculate terms in parentheses: -((+2x^2+36x-6x-108)), so:

(+2x^2+36x-6x-108)

We get rid of parentheses

2x^2+36x-6x-108

We add all the numbers together, and all the variables

2x^2+30x-108

Back to the equation:

-(2x^2+30x-108)


We get rid of parentheses

-2x^2-30x+108+2039=0

We add all the numbers together, and all the variables

-2x^2-30x+2147=0

a = -2; b = -30; c = +2147;
Δ = b2-4ac
Δ = -302-4·(-2)·2147
Δ = 18076
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:

$\sqrt{\Delta}=\sqrt{18076}=\sqrt{4*4519}=\sqrt{4}*\sqrt{4519}=2\sqrt{4519}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{4519}}{2*-2}=\frac{30-2\sqrt{4519}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{4519}}{2*-2}=\frac{30+2\sqrt{4519}}{-4}
$