0=6x^2+5x-36

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

0=6x^2+5x-36

We move all terms to the left:

0-(6x^2+5x-36)=0

We add all the numbers together, and all the variables

-(6x^2+5x-36)=0

We get rid of parentheses

-6x^2-5x+36=0

a = -6; b = -5; c = +36;
Δ = b2-4ac
Δ = -52-4·(-6)·36
Δ = 889
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{889}}{2*-6}=\frac{5-\sqrt{889}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{889}}{2*-6}=\frac{5+\sqrt{889}}{-12}
$