8x^2-5x-160=0

Solution for 8x^2-5x-160=0 equation:

8x^2-5x-160=0

a = 8; b = -5; c = -160;
Δ = b2-4ac
Δ = -52-4·8·(-160)
Δ = 5145
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:

$\sqrt{\Delta}=\sqrt{5145}=\sqrt{49*105}=\sqrt{49}*\sqrt{105}=7\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-7\sqrt{105}}{2*8}=\frac{5-7\sqrt{105}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+7\sqrt{105}}{2*8}=\frac{5+7\sqrt{105}}{16}
$