(2x+14)(x+3)=117

Solution for (2x+14)(x+3)=117 equation:

(2x+14)(x+3)=117

We move all terms to the left:

(2x+14)(x+3)-(117)=0

We multiply parentheses ..

(+2x^2+6x+14x+42)-117=0

We get rid of parentheses

2x^2+6x+14x+42-117=0

We add all the numbers together, and all the variables

2x^2+20x-75=0

a = 2; b = 20; c = -75;
Δ = b2-4ac
Δ = 202-4·2·(-75)
Δ = 1000
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:

$\sqrt{\Delta}=\sqrt{1000}=\sqrt{100*10}=\sqrt{100}*\sqrt{10}=10\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-10\sqrt{10}}{2*2}=\frac{-20-10\sqrt{10}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+10\sqrt{10}}{2*2}=\frac{-20+10\sqrt{10}}{4}
$