29x^2-14x-16=0

Solution for 29x^2-14x-16=0 equation:

29x^2-14x-16=0

a = 29; b = -14; c = -16;
Δ = b2-4ac
Δ = -142-4·29·(-16)
Δ = 2052
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:

$\sqrt{\Delta}=\sqrt{2052}=\sqrt{36*57}=\sqrt{36}*\sqrt{57}=6\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-6\sqrt{57}}{2*29}=\frac{14-6\sqrt{57}}{58}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+6\sqrt{57}}{2*29}=\frac{14+6\sqrt{57}}{58}
$