(2x+40)(x+6)=162(2)

Solution for (2x+40)(x+6)=162(2) equation:

(2x+40)(x+6)=162(2)

We move all terms to the left:

(2x+40)(x+6)-(162(2))=0

determiningTheFunctionDomain
(2x+40)(x+6)-1622=0

We multiply parentheses ..

(+2x^2+12x+40x+240)-1622=0

We get rid of parentheses

2x^2+12x+40x+240-1622=0

We add all the numbers together, and all the variables

2x^2+52x-1382=0

a = 2; b = 52; c = -1382;
Δ = b2-4ac
Δ = 522-4·2·(-1382)
Δ = 13760
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:

$\sqrt{\Delta}=\sqrt{13760}=\sqrt{64*215}=\sqrt{64}*\sqrt{215}=8\sqrt{215}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-8\sqrt{215}}{2*2}=\frac{-52-8\sqrt{215}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+8\sqrt{215}}{2*2}=\frac{-52+8\sqrt{215}}{4}
$