x(x+4)=x+14

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

x(x+4)=x+14

We move all terms to the left:

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

We multiply parentheses

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

We get rid of parentheses

x^2+4x-x-14=0

We add all the numbers together, and all the variables

x^2+3x-14=0

a = 1; b = 3; c = -14;
Δ = b2-4ac
Δ = 32-4·1·(-14)
Δ = 65
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{-(3)-\sqrt{65}}{2*1}=\frac{-3-\sqrt{65}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{65}}{2*1}=\frac{-3+\sqrt{65}}{2}
$