4x^2-32x-448=0

Solution for 4x^2-32x-448=0 equation:

4x^2-32x-448=0

a = 4; b = -32; c = -448;
Δ = b2-4ac
Δ = -322-4·4·(-448)
Δ = 8192
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:

$\sqrt{\Delta}=\sqrt{8192}=\sqrt{4096*2}=\sqrt{4096}*\sqrt{2}=64\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-64\sqrt{2}}{2*4}=\frac{32-64\sqrt{2}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+64\sqrt{2}}{2*4}=\frac{32+64\sqrt{2}}{8}
$