64x^2-16x-39=0

Solution for 64x^2-16x-39=0 equation:

64x^2-16x-39=0

a = 64; b = -16; c = -39;
Δ = b2-4ac
Δ = -162-4·64·(-39)
Δ = 10240
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:

$\sqrt{\Delta}=\sqrt{10240}=\sqrt{1024*10}=\sqrt{1024}*\sqrt{10}=32\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-32\sqrt{10}}{2*64}=\frac{16-32\sqrt{10}}{128}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+32\sqrt{10}}{2*64}=\frac{16+32\sqrt{10}}{128}
$