35=6c^2-30c-36

Solution for 35=6c^2-30c-36 equation:

35=6c^2-30c-36

We move all terms to the left:

35-(6c^2-30c-36)=0

We get rid of parentheses

-6c^2+30c+36+35=0

We add all the numbers together, and all the variables

-6c^2+30c+71=0

a = -6; b = 30; c = +71;
Δ = b2-4ac
Δ = 302-4·(-6)·71
Δ = 2604
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2604}=\sqrt{4*651}=\sqrt{4}*\sqrt{651}=2\sqrt{651}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{651}}{2*-6}=\frac{-30-2\sqrt{651}}{-12}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{651}}{2*-6}=\frac{-30+2\sqrt{651}}{-12}
$