17x^2-160x-400=0

Solution for 17x^2-160x-400=0 equation:

17x^2-160x-400=0

a = 17; b = -160; c = -400;
Δ = b2-4ac
Δ = -1602-4·17·(-400)
Δ = 52800
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:

$\sqrt{\Delta}=\sqrt{52800}=\sqrt{1600*33}=\sqrt{1600}*\sqrt{33}=40\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-160)-40\sqrt{33}}{2*17}=\frac{160-40\sqrt{33}}{34}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-160)+40\sqrt{33}}{2*17}=\frac{160+40\sqrt{33}}{34}
$