6x^2+36X+5=0

Solution for 6x^2+36X+5=0 equation:

6x^2+36x+5=0

a = 6; b = 36; c = +5;
Δ = b2-4ac
Δ = 362-4·6·5
Δ = 1176
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:

$\sqrt{\Delta}=\sqrt{1176}=\sqrt{196*6}=\sqrt{196}*\sqrt{6}=14\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-14\sqrt{6}}{2*6}=\frac{-36-14\sqrt{6}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+14\sqrt{6}}{2*6}=\frac{-36+14\sqrt{6}}{12}
$