64x^2+16x-271=0

Solution for 64x^2+16x-271=0 equation:

64x^2+16x-271=0

a = 64; b = 16; c = -271;
Δ = b2-4ac
Δ = 162-4·64·(-271)
Δ = 69632
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:

$\sqrt{\Delta}=\sqrt{69632}=\sqrt{4096*17}=\sqrt{4096}*\sqrt{17}=64\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-64\sqrt{17}}{2*64}=\frac{-16-64\sqrt{17}}{128}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+64\sqrt{17}}{2*64}=\frac{-16+64\sqrt{17}}{128}
$