5x^2-2x-17=0

Solution for 5x^2-2x-17=0 equation:

5x^2-2x-17=0

a = 5; b = -2; c = -17;
Δ = b2-4ac
Δ = -22-4·5·(-17)
Δ = 344
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:

$\sqrt{\Delta}=\sqrt{344}=\sqrt{4*86}=\sqrt{4}*\sqrt{86}=2\sqrt{86}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{86}}{2*5}=\frac{2-2\sqrt{86}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{86}}{2*5}=\frac{2+2\sqrt{86}}{10}
$