x(x+4)2=7

Solution for x(x+4)2=7 equation:

x(x+4)2=7

We move all terms to the left:

x(x+4)2-(7)=0

We multiply parentheses

2x^2+8x-7=0

a = 2; b = 8; c = -7;
Δ = b2-4ac
Δ = 82-4·2·(-7)
Δ = 120
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:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{30}}{2*2}=\frac{-8-2\sqrt{30}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{30}}{2*2}=\frac{-8+2\sqrt{30}}{4}
$