6x^2+36x+29=0

Solution for 6x^2+36x+29=0 equation:

6x^2+36x+29=0

a = 6; b = 36; c = +29;
Δ = b2-4ac
Δ = 362-4·6·29
Δ = 600
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:

$\sqrt{\Delta}=\sqrt{600}=\sqrt{100*6}=\sqrt{100}*\sqrt{6}=10\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-10\sqrt{6}}{2*6}=\frac{-36-10\sqrt{6}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+10\sqrt{6}}{2*6}=\frac{-36+10\sqrt{6}}{12}
$