-16x^2+80x+1=0

Solution for -16x^2+80x+1=0 equation:

-16x^2+80x+1=0

a = -16; b = 80; c = +1;
Δ = b2-4ac
Δ = 802-4·(-16)·1
Δ = 6464
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:

$\sqrt{\Delta}=\sqrt{6464}=\sqrt{64*101}=\sqrt{64}*\sqrt{101}=8\sqrt{101}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-8\sqrt{101}}{2*-16}=\frac{-80-8\sqrt{101}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+8\sqrt{101}}{2*-16}=\frac{-80+8\sqrt{101}}{-32}
$