7x^2-16x-1=0

Solution for 7x^2-16x-1=0 equation:

7x^2-16x-1=0

a = 7; b = -16; c = -1;
Δ = b2-4ac
Δ = -162-4·7·(-1)
Δ = 284
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:

$\sqrt{\Delta}=\sqrt{284}=\sqrt{4*71}=\sqrt{4}*\sqrt{71}=2\sqrt{71}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{71}}{2*7}=\frac{16-2\sqrt{71}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{71}}{2*7}=\frac{16+2\sqrt{71}}{14}
$