(2x+14)(x+4)=216

Solution for (2x+14)(x+4)=216 equation:

(2x+14)(x+4)=216

We move all terms to the left:

(2x+14)(x+4)-(216)=0

We multiply parentheses ..

(+2x^2+8x+14x+56)-216=0

We get rid of parentheses

2x^2+8x+14x+56-216=0

We add all the numbers together, and all the variables

2x^2+22x-160=0

a = 2; b = 22; c = -160;
Δ = b2-4ac
Δ = 222-4·2·(-160)
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-42}{2*2}=\frac{-64}{4}
=-16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+42}{2*2}=\frac{20}{4}
=5
$