(X+6)(2x+6)=416

Solution for (X+6)(2x+6)=416 equation:

(X+6)(2X+6)=416

We move all terms to the left:

(X+6)(2X+6)-(416)=0

We multiply parentheses ..

(+2X^2+6X+12X+36)-416=0

We get rid of parentheses

2X^2+6X+12X+36-416=0

We add all the numbers together, and all the variables

2X^2+18X-380=0

a = 2; b = 18; c = -380;
Δ = b2-4ac
Δ = 182-4·2·(-380)
Δ = 3364
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3364}=58$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-58}{2*2}=\frac{-76}{4}
=-19
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+58}{2*2}=\frac{40}{4}
=10
$