(20)(39)=(x+8)(2x-6)

Solution for (20)(39)=(x+8)(2x-6) equation:

(20)(39)=(x+8)(2x-6)

We move all terms to the left:

(20)(39)-((x+8)(2x-6))=0

We multiply parentheses ..

-((+2x^2-6x+16x-48))+2039=0


We calculate terms in parentheses: -((+2x^2-6x+16x-48)), so:

(+2x^2-6x+16x-48)

We get rid of parentheses

2x^2-6x+16x-48

We add all the numbers together, and all the variables

2x^2+10x-48

Back to the equation:

-(2x^2+10x-48)


We get rid of parentheses

-2x^2-10x+48+2039=0

We add all the numbers together, and all the variables

-2x^2-10x+2087=0

a = -2; b = -10; c = +2087;
Δ = b2-4ac
Δ = -102-4·(-2)·2087
Δ = 16796
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:

$\sqrt{\Delta}=\sqrt{16796}=\sqrt{4*4199}=\sqrt{4}*\sqrt{4199}=2\sqrt{4199}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{4199}}{2*-2}=\frac{10-2\sqrt{4199}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{4199}}{2*-2}=\frac{10+2\sqrt{4199}}{-4}
$