17x^2-16x-80=0

Solution for 17x^2-16x-80=0 equation:

17x^2-16x-80=0

a = 17; b = -16; c = -80;
Δ = b2-4ac
Δ = -162-4·17·(-80)
Δ = 5696
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:

$\sqrt{\Delta}=\sqrt{5696}=\sqrt{64*89}=\sqrt{64}*\sqrt{89}=8\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-8\sqrt{89}}{2*17}=\frac{16-8\sqrt{89}}{34}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+8\sqrt{89}}{2*17}=\frac{16+8\sqrt{89}}{34}
$