X^2+64x+128=0

Solution for X^2+64x+128=0 equation:

X^2+64X+128=0

a = 1; b = 64; c = +128;
Δ = b2-4ac
Δ = 642-4·1·128
Δ = 3584
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:

$\sqrt{\Delta}=\sqrt{3584}=\sqrt{256*14}=\sqrt{256}*\sqrt{14}=16\sqrt{14}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-16\sqrt{14}}{2*1}=\frac{-64-16\sqrt{14}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+16\sqrt{14}}{2*1}=\frac{-64+16\sqrt{14}}{2}
$