4a^2-8a-17=0

Solution for 4a^2-8a-17=0 equation:

4a^2-8a-17=0

a = 4; b = -8; c = -17;
Δ = b2-4ac
Δ = -82-4·4·(-17)
Δ = 336
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{21}}{2*4}=\frac{8-4\sqrt{21}}{8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{21}}{2*4}=\frac{8+4\sqrt{21}}{8}
$