3x^2-6x-29=0

Solution for 3x^2-6x-29=0 equation:

3x^2-6x-29=0

a = 3; b = -6; c = -29;
Δ = b2-4ac
Δ = -62-4·3·(-29)
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-8\sqrt{6}}{2*3}=\frac{6-8\sqrt{6}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+8\sqrt{6}}{2*3}=\frac{6+8\sqrt{6}}{6}
$