0=-6x^2+36x+16

Solution for 0=-6x^2+36x+16 equation:

0=-6x^2+36x+16

We move all terms to the left:

0-(-6x^2+36x+16)=0

We add all the numbers together, and all the variables

-(-6x^2+36x+16)=0

We get rid of parentheses

6x^2-36x-16=0

a = 6; b = -36; c = -16;
Δ = b2-4ac
Δ = -362-4·6·(-16)
Δ = 1680
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:

$\sqrt{\Delta}=\sqrt{1680}=\sqrt{16*105}=\sqrt{16}*\sqrt{105}=4\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{105}}{2*6}=\frac{36-4\sqrt{105}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{105}}{2*6}=\frac{36+4\sqrt{105}}{12}
$