2x(2x+4)=448

Solution for 2x(2x+4)=448 equation:

2x(2x+4)=448

We move all terms to the left:

2x(2x+4)-(448)=0

We multiply parentheses

4x^2+8x-448=0

a = 4; b = 8; c = -448;
Δ = b2-4ac
Δ = 82-4·4·(-448)
Δ = 7232
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:

$\sqrt{\Delta}=\sqrt{7232}=\sqrt{64*113}=\sqrt{64}*\sqrt{113}=8\sqrt{113}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8\sqrt{113}}{2*4}=\frac{-8-8\sqrt{113}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8\sqrt{113}}{2*4}=\frac{-8+8\sqrt{113}}{8}
$