0=6x^2+x-5

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

0=6x^2+x-5

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

-6x^2-x+5=0

We add all the numbers together, and all the variables

-6x^2-1x+5=0

a = -6; b = -1; c = +5;
Δ = b2-4ac
Δ = -12-4·(-6)·5
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-11}{2*-6}=\frac{-10}{-12}
=5/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+11}{2*-6}=\frac{12}{-12}
=-1
$