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

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

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

We move all terms to the left:

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

determiningTheFunctionDomain
(x+8)(2x-6)-3920=0

We multiply parentheses ..

(+2x^2-6x+16x-48)-3920=0

We get rid of parentheses

2x^2-6x+16x-48-3920=0

We add all the numbers together, and all the variables

2x^2+10x-3968=0

a = 2; b = 10; c = -3968;
Δ = b2-4ac
Δ = 102-4·2·(-3968)
Δ = 31844
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:

$\sqrt{\Delta}=\sqrt{31844}=\sqrt{4*7961}=\sqrt{4}*\sqrt{7961}=2\sqrt{7961}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{7961}}{2*2}=\frac{-10-2\sqrt{7961}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{7961}}{2*2}=\frac{-10+2\sqrt{7961}}{4}
$