4a^2-17a-34=0

Solution for 4a^2-17a-34=0 equation:

4a^2-17a-34=0

a = 4; b = -17; c = -34;
Δ = b2-4ac
Δ = -172-4·4·(-34)
Δ = 833
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:

$\sqrt{\Delta}=\sqrt{833}=\sqrt{49*17}=\sqrt{49}*\sqrt{17}=7\sqrt{17}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-7\sqrt{17}}{2*4}=\frac{17-7\sqrt{17}}{8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+7\sqrt{17}}{2*4}=\frac{17+7\sqrt{17}}{8}
$