16x^2-80x-25=0

Solution for 16x^2-80x-25=0 equation:

16x^2-80x-25=0

a = 16; b = -80; c = -25;
Δ = b2-4ac
Δ = -802-4·16·(-25)
Δ = 8000
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:

$\sqrt{\Delta}=\sqrt{8000}=\sqrt{1600*5}=\sqrt{1600}*\sqrt{5}=40\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-40\sqrt{5}}{2*16}=\frac{80-40\sqrt{5}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+40\sqrt{5}}{2*16}=\frac{80+40\sqrt{5}}{32}
$