8x^2+20x-17=0

Solution for 8x^2+20x-17=0 equation:

8x^2+20x-17=0

a = 8; b = 20; c = -17;
Δ = b2-4ac
Δ = 202-4·8·(-17)
Δ = 944
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:

$\sqrt{\Delta}=\sqrt{944}=\sqrt{16*59}=\sqrt{16}*\sqrt{59}=4\sqrt{59}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{59}}{2*8}=\frac{-20-4\sqrt{59}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{59}}{2*8}=\frac{-20+4\sqrt{59}}{16}
$