X(x+8)=448

Solution for X(x+8)=448 equation:

X(X+8)=448

We move all terms to the left:

X(X+8)-(448)=0

We multiply parentheses

X^2+8X-448=0

a = 1; b = 8; c = -448;
Δ = b2-4ac
Δ = 82-4·1·(-448)
Δ = 1856
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:

$\sqrt{\Delta}=\sqrt{1856}=\sqrt{64*29}=\sqrt{64}*\sqrt{29}=8\sqrt{29}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8\sqrt{29}}{2*1}=\frac{-8-8\sqrt{29}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8\sqrt{29}}{2*1}=\frac{-8+8\sqrt{29}}{2}
$