x(x+14)=47

Solution for x(x+14)=47 equation:

x(x+14)=47

We move all terms to the left:

x(x+14)-(47)=0

We multiply parentheses

x^2+14x-47=0

a = 1; b = 14; c = -47;
Δ = b2-4ac
Δ = 142-4·1·(-47)
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-8\sqrt{6}}{2*1}=\frac{-14-8\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+8\sqrt{6}}{2*1}=\frac{-14+8\sqrt{6}}{2}
$