2x(x+4)+x=14

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

2x(x+4)+x=14

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We add all the numbers together, and all the variables

2x^2+9x-14=0

a = 2; b = 9; c = -14;
Δ = b2-4ac
Δ = 92-4·2·(-14)
Δ = 193
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{193}}{2*2}=\frac{-9-\sqrt{193}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{193}}{2*2}=\frac{-9+\sqrt{193}}{4}
$