2x(x+4)=14+x

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

2x(x+4)=14+x

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

2x^2+7x-14=0

a = 2; b = 7; c = -14;
Δ = b2-4ac
Δ = 72-4·2·(-14)
Δ = 161
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{-(7)-\sqrt{161}}{2*2}=\frac{-7-\sqrt{161}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{161}}{2*2}=\frac{-7+\sqrt{161}}{4}
$