-16x^2+5x+29=0

Solution for -16x^2+5x+29=0 equation:

-16x^2+5x+29=0

a = -16; b = 5; c = +29;
Δ = b2-4ac
Δ = 52-4·(-16)·29
Δ = 1881
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:

$\sqrt{\Delta}=\sqrt{1881}=\sqrt{9*209}=\sqrt{9}*\sqrt{209}=3\sqrt{209}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-3\sqrt{209}}{2*-16}=\frac{-5-3\sqrt{209}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+3\sqrt{209}}{2*-16}=\frac{-5+3\sqrt{209}}{-32}
$